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TABLE OF CONTENTS NEXT
O M G PREVIOUS NEXT VISION  A premier university in CALABARZON, offering academic programs and related services designed t...
V G O PREVIOUS NEXT MISSION The University shall primarily provide advanced education, professional, technological and voc...
V O M PREVIOUS NEXT GOALS In pursuit of the college vision/mission the College of Education is committed to develop the fu...
V G M PREVIOUS NEXT <ul><li>OBJECTIVES OF BACHELOR OF SECONDARY EDUCATION </li></ul><ul><li>  </li></ul><ul><li>Produce gr...
FOREWORD This Teacher’s Visual Presentation Hand-out entitled  “Workbook in Solving Algebraic Expression for Second Year H...
<ul><li>The students are provided with guidance and assistance of selected faculty members of the College through the sele...
<ul><li>  FOR-IAN V. SANDOVAL </li></ul><ul><li>  Computer Instructor / Adviser  </li></ul><ul><li>  Educational Technolog...
PREVIOUS NEXT ACKNOWLEDGEMENT The authors wish to acknowledge the following persons who gave them the inspiration and the ...
Dr. Corazon N. San Agustin, an Educational Technology professor for being the first one who teach us to make a module. Fri...
INTRODUCTION This workbook is composed of activities in understanding and analyzing different terminologies and concepts i...
GENERAL OBJECTIVES In this workbook entitled  “Workbook in Solving Algebraic Expression for Second Year High School Studen...
7.  Recognize the different terms of a polynomial. 8.  Write a monomial, binomial and trinomial equation. 9.  Specify if t...
16.  Recall the different degree of polynomial. 17. Have confidence to their self to find the correct answer. 18. Improve ...
TABLE OF CONTENTS Vision, Mission, Goals and Objectives Foreword Acknowledgement Introduction General Objectives PREVIOUS ...
PREVIOUS NEXT Chapter I Understanding and Analyzing Different  Terminologies in Algebraic Expression Pre Test I Activity 1...
PREVIOUS NEXT Chapter II Solving Algebraic Expression Using  Fundamental Operations Post Test I Activity 10 Pre Test II Ac...
PREVIOUS NEXT Activity 18 Activity 19 Activity 20 Activity 21 Post Test II Activity 15 Activity 17 Activity 16
PREVIOUS NEXT Activity 24 Activity 25 Activity 26 Activity 27 Activity 28 Chapter III Using Synthetic Method in Solving  A...
PREVIOUS NEXT Activity 32 Activity 33 Activity 34 Activity 35 Activity 36 Post Test III Activity 31 Activity 30 Activity 29
PREVIOUS NEXT Chapter IV Simple Types of Factoring of  Algebraic Expression Pre Test IV Activity 37 Activity 38 Activity 3...
PREVIOUS NEXT Post Test IV Activity 44 Activity 45 Activity 46 Activity 47 Activity 48 Activity 49 Activity 50 Activity 51...
About the Author References PREVIOUS NEXT Final
Pre Test I Name: __________________________Score: _____________Date: _______________ <ul><ul><ul><ul><li>Year and Section:...
<ul><li>A. Instruction: Tell whether the statements below are true or false by writing  A  if the statements is correct an...
<ul><li>C. Instruction: Identify the terms and terminologies stated in each number. Write your answer in the space provide...
<ul><li>F. Instruction: Identify the polynomials in column  A  to its corresponding terms in column  B . Write your answer...
<ul><li>G . Instruction: Identify the polynomial in column  A  to its corresponding degree in column  B . Write your answe...
<ul><li>I.  Instruction: Identify the degrees of polynomials. Write your answer in the space provided. </li></ul><ul><li> ...
Answers QUESTIONS QUESTIONS QUESTIONS QUESTIONS A.  1.B 2.B 3.B 4.B 5.B B.  1. e 2. b 3. a 4. c 5. d C.  1. constant 2.Lit...
QUESTIONS QUESTIONS QUESTIONS QUESTIONS QUESTIONS G .  1. c 2. a 3. e 4. d 5. b H .  1. c 2.c 3.c 4.c 5.c F .  1. binomial...
<ul><li>Activity 1 </li></ul><ul><li>Name: __________________Score:_____________Date: ____________ </li></ul><ul><li>Year ...
<ul><li>Answers </li></ul><ul><li>1. B </li></ul><ul><li>2. B </li></ul><ul><li>3. B </li></ul><ul><li>4. B </li></ul><ul>...
<ul><li>Activity 2 </li></ul><ul><li>Name:__________________________Score:_____________Date:_______________ </li></ul><ul>...
<ul><li>Answers </li></ul><ul><li>1. f </li></ul><ul><li>2. i </li></ul><ul><li>3. a </li></ul><ul><li>4. g </li></ul><ul>...
Activity 3 Name: _______________________Score: ___________Date:__________ Year and Section: _____________Teacher:_________...
Previous Next Answers __________6. It is a positive or negative integer, written in the upper right of letters or symbols....
<ul><li>Answers </li></ul><ul><li>1.constant </li></ul><ul><li>2.Literal coefficient </li></ul><ul><li>3.monomial </li></u...
Activity 4 Name:______________________Score:_________Date:_____________ Year and Section:_________________Teacher:________...
<ul><li>Answers </li></ul><ul><li>1.B </li></ul><ul><li>2.A </li></ul><ul><li>3.B </li></ul><ul><li>4.C </li></ul><ul><li>...
Activity 5 Name: ______________________Score:_________Date:___________ Year and Section:________________ Teacher: ________...
<ul><li>Answers </li></ul><ul><li>1.e </li></ul><ul><li>2.a </li></ul><ul><li>3.j </li></ul><ul><li>4.h </li></ul><ul><li>...
Activity 6   Name:____________________Score:_____________Date:____________   Year and Section:____________________Teacher:...
Answers <ul><li>1.binomial </li></ul><ul><li>2.trinomial </li></ul><ul><li>3.monomial </li></ul><ul><li>4.binomial </li></...
Activity 7 Name: ________________________Score:_____________Date:_____________ Year and Section:___________________Teacher...
Answers <ul><li>1.a </li></ul><ul><li>2.i </li></ul><ul><li>3.g </li></ul><ul><li>4.h </li></ul><ul><li>5.b </li></ul><ul>...
Activity 8 Name:_______________________Score:_____________Date:____________ Year and Section:____________________Teacher:_...
<ul><li>4 . x⁵ - y⁸ </li></ul><ul><li>  a. 6 th  degree b. 7 th  degree c. 8 th  degree </li></ul><ul><li>5. 5x² + 4y⁶ </l...
Answers <ul><li>1.c </li></ul><ul><li>2.c </li></ul><ul><li>3.c </li></ul><ul><li>4.c </li></ul><ul><li>5.c </li></ul><ul>...
<ul><li>Instruction: Identify the degree of the given polynomials. Write your answer in the space provided. </li></ul><ul>...
Answers <ul><li>1.8 th  degree </li></ul><ul><li>2.9 th  degree </li></ul><ul><li>3.11 th  degree </li></ul><ul><li>4.9 th...
Post Test I Name:__________________________Score:_____________Date:_______________ Year and Section:____________________Te...
A. Instruction: Identify the terms and terminologies in each number. Encircle the letter of your answer.   1. It is a lett...
6. It is a number in a given polynomial. a. Constant b. Variable c. Exponent 7. Algebraic Expression involves non-negative...
<ul><li>B. Identify the terms of the polynomials. Write  R  if the given polynomial is monomial,  M  if the given polynomi...
<ul><li>C. Identify the degree of polynomials. Write your answer in the space provided. </li></ul><ul><li>  </li></ul><ul>...
<ul><li>D. True or False. Write  E  if the statement is correct and  R  if the statement is incorrect. Write your answer i...
Answers <ul><li>A.  </li></ul><ul><li>1.a </li></ul><ul><li>2.b </li></ul><ul><li>3.a </li></ul><ul><li>4.c </li></ul><ul>...
Pre Test II Name:__________________________Score:_____________ Date:____________ Year and Section:__________________Teache...
INSTRUCTION: Write your solution in performing the given operations. 1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c) 2. (3x – 8y + 6...
11. (-5x² – 4x + 2y) – (6x² - x + 3)   12. (2a³ + a² + 4a – 3) – (4a³ - 8a² + 2a + 6)   13. (16a + 9b) – (8a + 2b)   14. (...
21. (88x – 44y) + (55x + 22y)   22. (37b + 49ab² - 28a³) + ( 34a³ - 32ab² - 25b)   23. (59x² + 49y) + (74x² + 54y)   24. 1...
31. 58xyz(34xz)   32. -14f²(62huv)   33. 28xy²(18x²)   34. 92a²b²c(57a³b²c²)   35. (x 2  + 7x + 10) ÷ (x – 5)   36. (2 3 a...
Answers Pre Test 31 - 40 Pre Test 21 - 30 Pre Test 11-20 Pre Test 1 - 10 A.  1. 14a 2  – 10b + 5c  2. x – y + 10z 3. 12x 3...
Activity 10 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
  _____1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c) _____2. (3x – 8y + 6z) + ( 7y – 2x + 4z) _____3. (5x³ + 2y²) + ( 7x³ - y²) __...
Answers Questions 1. s 2. p 3. l 4. t 5. q 6. m 7. o 8. h 9. k 10. g
Activity 11 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
6. (3b + 4ab² - 2a³) + ( 3a³ - 3ab² - 2b)   7. (5x² + 4y) + (7x² + 5y)   8. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y)   9. (3x...
Answers Questions 1- 5 Questions 6 - 15 1. 8a 2  + 8ab – 4c 2. 7x 2  + 5xy – 7y 3. 11a 3  – ab 2  – c  4. 3a – 3ab – 10b  ...
Activity 12 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers Questions 1. 2y 2  – 7x + 4y 2. 13t – 5x – 2u  3. 7a 3  + ab 2  – 8c 4. -6a + 4ab – 2c  5. -2a + 2x 6. 12t 2  + 2t...
Activity 13 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers Questions 1. 4x 2  – 6x + 15 2. 3a 2  – 5a – 2  3. -8a – 14b + 7c 4. -4a + 5b + c 5. -11x 2  – 3x + 2y – 3  6. -2a...
Activity 14 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
___________ 6. (-5x + 7y – z) – (6x – 7y + 2z) is equal to 11x + 14y – 3z. ___________ 7. In equation (-11x³ - 5x² - 7x -6...
Answers Questions 1 - 5 Questions 6 - 10 1. + 2. + 3.  + 4. - 5.  + 6.  - 7.  + 8.  + 9.  + 10.  -
Activity 15 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers Questions 1. –l 2  + 9m + 10y  2. 8x + 2t – 6u  3. 3a 3  – ab 2  + 8c 4. 6a 2  – ab + 2c 5. -10a + 12x 6. 24t 2  –...
Activity 16 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
8. 3x 3 (4y 2 ) 9. (5a + 7b – 8c)(8a + 4c) 10. (9u + 5v – 2z)(5u + 2v – 2u) 11. (-5x 2 y 3 w)(2x + y)   12. (4x + 2y)(5x 3...
Answers Questions 1 - 7 Questions 8- 15 1. 20xy 2  – 10y – 8xyz 2  – 6z 2 2. -9a 5 b 3 cd 2  – 9ab 3. -12bc – 3c 2  – 32b ...
Activity 17 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
    Across 1. (2xy)(9x²)(7y) 4. (5u²)(5u) 5. (9w)(5) 7. (zmn)(z³m²n) 8  (3x²)(3x²y) 9. (26a²)(2a²)   Down  1. (6u²)(3u) 2....
Answers Questions  Across  1. 126x 3 y 2 4. 25u 3 5. 45w 7. z 4 m 3 n 2 8. 9x 4 y 9. 52a 2 Down 1. 18u 3 2. 114 3. y 2 z 2...
Activity 18 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
<ul><li>_____8. 9i⁶l²(6u³v³) c5. 8c 2 t </li></ul><ul><li>_____9. 5xyz (4xz) c6. m 2 op 2 </li></ul><ul><li>_____10. -14f²...
Answers Questions 1 - 7 Questions 8 - 15 1. a4 2. c5 3. f7 4. c6 5. h8 6. d1 7. a3 8. g5 9. b5 10. d2 11. a1 12. b2 13. b6...
Activity 19 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers Questions  1. x – 5  2. y + 1 3. 4 4. x 5. X + 12 r. 70 6. 8a 4 b/9c 7. x – 10  8. a + 1 9. 4t 3  – 3t 2  + 2t + 5...
Activity 20 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
8. (2a 2 b 2 ) ÷ (a 2 b 2 ) 9. (4x 2 y 3  – 24xy 4 ) ÷ (2xy 2 ) 10. (12x 3 y 4  + 18x 4 y 2  – 36xy 3 ) ÷ (3x 2 y 2 ) 11. ...
Answers Questions 1 - 7 Questions 8- 15
Activity 21 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers Questions
Post Test II Name: __________________________Score: _____________Date:______________ Year and Section:____________________...
<ul><li>INSTRUCTION: Perform the indicated operations and show your solutions. </li></ul><ul><li>Add the following Algebra...
<ul><li>B. Subtract the following Algebraic Expressions. </li></ul><ul><li>(33x + 12y + 27z) – (46x – 15y + 23z) </li></ul...
C. Multiply the following Algebraic Expressions. 11. 6x²(25xy) 12. 42c²(21t) 13. 19x(36xy) 14. 34m²p(86op) 15. 13x(85z) 16...
D. Divide the following Algebraic Expressions. 26. (x⁵ )  ÷ (x ² ) 27. (-4 ²x ) ÷ (2 ³x ) 28. (16x 8 ) ÷ (4x 3 ) 29. (10m ...
Answers Post Test A A.  1. 10a 2  + 5a + 6ab + 4c 2. 28x 2  + 26xy – 16y  3. 117a 3  – 8ab 2  – 9c 4. 45a – 36ab – 111b  5...
Answers Post Test B B. 1. -13x – 3y + 50z  2. 148x 3  – 6y 2  + 118z 3. 26x – 3y – 5z 4. 60x  6 + 112y 5.  10a + 20c 6. 28...
Answers Post Test C 11. 150x 3 y 12.882c 2 t 13. 684x 2 y 14. 2924m 2 op 2 15. 1105xz 16.306j 10 k 2 17. -504h 2 l 5 t 2 1...
Answers Post Test D
Pre Test III Name:__________________________Score:_____________Date:_____________ Year and Section:__________________Teach...
<ul><li>INSTRUCTION: Solve the “SPECIAL PRODUCTS” of the following equations. </li></ul><ul><li>Show your solution and box...
11. (f +2) (f – 8) 12. (w + 4) (w + 11) 13. (s + 5) (s + 6) 14. (c + 10) (c – 3) 15. (a + 8) (a + 9) 16. (i + 25) (i – 3) ...
<ul><li>21.  (ax – 2xy)  3 </li></ul><ul><li>22.  (xy 2   + wz 2 )  3 </li></ul><ul><li>23.  (7x 2 + y 4 )  3 </li></ul><u...
Answers 1. f⁴ - 4fc² + 4c² 2. x ²  + 26x + 169 3. 256a 4  + 32a 2  + b 2 4. 4p 2  + 8pq + 4q 2 5. 4a 2m  + 12a m  z + 9q 2...
Activity 22 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. 25 2x 2. 16y 6 3. x 8 y 4 4. a 4 c 2e e 2m 5. k 20  m 6n 6. 16j 2n h 2x+2 7. 100m 2 8. 16x 2 y 2 z 2 9. 625m 2n...
Activity 23 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. V 2. A 3. R 4. I 5. A 6. B 7. L 8. E 9. S Questions
Activity 24 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
8. (3a 4 b 3 )  2 9. (53x 2 )  2 10. (13x 2 y 2 )  2 11. (4n x+1 )  2 12. (5ab 3 )  2 13. (21t 3 w 3 )  2 14. (3b a+2 m 2 ...
Answers 1. 49x 6 2. u 2 v 4 3. 100x 2 4. 64y 2 5.x 2 y 2 6. 36m 12x 7. 169a 2x b 4y c 10z 8. 9a 8 b 6 9. 2809x 4 10. 169x ...
Activity 25 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
__________6. The product of the third term of the equation 4c(5a 2  + 2c 2  – 5d + 3b) is -20cd.     __________7. In 2 x +...
Answers 1. a 2. A 3. a 4. A 5. a 6. A 7. a 8. A 9. a 10. a Questions 1 - 5  Questions 6 - 10
Activity 26 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. xy 2  + x 3 y + 6x 2. 4a 3  – 7a 2  – 2a 3. 6x 3  + 8x 2  + 18x 4. 6 r2 st + 60r 3 t 5. a 2 b 2 c – a 2 bc + ab...
Activity 27 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. 56x 3 y 2  + 378x 3  + 14x 6 2. 2y 3  + 8y 2  - 42 3. 63d 3 p + 189d 2 p 4. 720p 3 q 2  – 15 p 2 qx 2 5. -28q 2...
Activity 28 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. 16a 2  + 8ab + b 2 2. 4x 2  + 12xy + 9y 2 3. 16u 2  + 24uv + 9v 2 4. 64a 2  + 48au + 9u 2 5. 25a 2  – 10 ab + b...
Activity 29 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
<ul><li>(2x -3y)  2 </li></ul><ul><li>(2x 2  + 6x)  2 </li></ul><ul><li>(27x 2  + y)  2 </li></ul><ul><li>(y 2  – 13y)  2 ...
Answers 1. y 3  – 18y +81  2. 4x 3  + 24x +36 3. x 4  + 2x 2  + 1 4. y 4  – 8y 3  + 16y 2 5. x 2  + 6x + 9 6. 9b 4  + 6b 3...
Activity 30 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. 25y 2  – 10y + 1 2. 4c 2  + 4cd + d 2 3. x 4  + 4x 2 y + 4y 2 4. 25a 2 t 2  – 10at + 1 5. 9x 4  +12x 4  + 4x 4 ...
Activity 31 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
8. (12c 2   – 6x 2 )  3 9. (3b 3   – 7y)  3 10. (6e 2  + 3j)  3   11. (9a 3  – 7m)  3   12. (4d 2   + 3f)  3   13. (3q 2  ...
Answers 1. x 3  + 3x 2 y + 3xy 2  + y 3 2. 8x 3  + 48x 2 y + 96xy 2  + 64y 3 3. 27x 9  + 135x 6 y + 225x 3 y 2  + 125y 3  ...
Activity 32 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. 8x 2  – 36x 2 y + 54xy 2  – 27y 3 2. x 2  – 6x 2  + 12x - 8 3. 8x 3  + 24ax 2  + 24a 2 x + 8a 3 4. 125x 3  – 22...
Activity 33 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. 27x 3  + 108x 2 y + 144xy 2  + 64y 3 2. 343x 6  + 147x 4 y 4  – 21x 2 y 8  + y 2 3. 64f 3  – 384f 2 y + 768fy 2...
Activity 34 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
8. (j 2  + 6) (j 2  + 8) 9. (e 3  + 2) (e 3  – 4) 10. (r 4  – 3) (r 4  + 5) 11. (3x + 8)(7x + 9) 12. (2x + 4)(4x + 6) 13. ...
Answers 1. a 2  + 109 + 16 2. l 2  + 15l + 54 3. e 2  + 12e + 35 4. t 2  + 8t + 12 5. h 2  + 8h + 15 6. x 2  + 6x + 8 7. m...
Activity 35 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
8. (w + 4) (w + 11) 9. (j + 5) (j – 3) 10. (x + 19) (x – 6) 11. (3x + 5) (2x + 35) 12. (3x 2  + 3) (3x 2  + 25) 13. (4a + ...
Answers 1. x 2  – 17x - 60 2. y 2  – y – 2  3. k 2  + 35 k + 150 4. a 2  + 2a – 24  5. x 2  – 6x – 27  6. m 2  + 13m + 40 ...
Activity 36 Name: __________________________Score: _____________Date:______________ Year and Section:____________________T...
Answers 1. i 2  + 22i - 75 2. i 2  + 22i - 75 3. 0 2  + 11o - 26 4. x 2  + 4x - 5 5. a 2  + 17a + 72 6. a 2  – 2a – 99  7....
Post Test III Name: __________________________Score: _____________Date:______________ Year and Section:___________________...
<ul><li>INSTRUCTION:  Solve the following polynomials and get their special products.  </li></ul><ul><li>Show  your soluti...
<ul><li>B. Cube the following binomials </li></ul><ul><li>(5ax – 23by) 3 </li></ul><ul><li>(2x – 6)  3 </li></ul><ul><li>(...
<ul><li>C. Solve the following equations. </li></ul><ul><li>a 2 (f 2  + a 2 y + 6) </li></ul><ul><li>m(6a 2  – 9a – 10) </...
<ul><li>(k + 5) (k – 18) </li></ul><ul><li>(q + 2) (q + 4)  </li></ul><ul><li>(y + 3) (y + 7) </li></ul><ul><li>(u + 15) (...
Answers 1. e 2 r 6 2. 25y 4 3. 144d 2 4. 49j 2 y 2 5. y 2 x 2 6. 49k 8x 7. 4w 29 y 4h z 6z 8. 144r 10 t 12 9. 676m 6a 10. ...
Answers 1. 12a 3 x 2  – 175a 2 bx 2 y + 7 935ab 2 xy 2  – 12 167b 3 y3  2. 8x 3  – 72x 2  + 216x - 216   3. 8f 3 x 3  + 24...
Answers 1. a 2 f 2  – a 4 y + 6a 2 2. 6a 2 m – 9am – 10m 3. 8x 4  + 4ax 2  + 32x 4. 6r 2 st + 60r 3 t + 9rs 5. m 2 n 2 o –...
Answers 16. k 2  – 13k - 90  17. q 2  + 6q + 8 18. y 2  + 10y + 21 19. u 2  + 13u - 30  20. x 4  – 2x 2  – 8  21. w 6  + 1...
Pre Test IV Name:  __________________________ Score:_____________Date:_______________ Year and Section: ________________ T...
A. Instruction: Tell whether if the common factor of the following polynomial is correct. Write  A  if the factor is corre...
C. Instruction: Factor the following algebraic expression. Get their common factor.  Write your answer in the space provid...
E. Instruction: Tell whether if the factor by grouping of the following polynomial is correct.  Write  A  if the factor is...
G. Instruction: Factor the following algebraic expressions by grouping. Write your answer  in the space provided.  1. 27x³...
<ul><li>Instruction: Factor the difference of the two squares of the given polynomials.  </li></ul><ul><li>Write your answ...
K. Instruction: Match polynomials in column  A  to its correct factor which is a perfect trinomial square in column  B .  ...
M. Instruction: Tell whether if the factor of the following equations is a factor of general quadratic trinomial. Write  A...
O. Instruction: Factoring the sum and difference of cubes of the following polynomials. Write the letter of your answer in...
A. 1. A 2. A 3. A 4. B 25(25x³ - 5y²) 5. A Answers B. 1. D 2. C 3. E 4. A 5. B C. 1. 2c 2 (3c 2  – 4c - )1 2. 2(b 3  – 2b ...
I. 1. (9a+16b 2 )(9a-16b 2 2.(5+13z)(5 -13z) 3. (11-10xy)(11+10xy) 4. (5m–6n)(5m+6n) 5. (8xy 2 –1) (8xy 2  +1) O. 1. (x-2)...
Activity 37 Name: _________________________Score:_________Date:___________ Year and Section: ________________ Teacher: ___...
Answers 1. A 2. A 3. B 8(3x 3  – 8y 3 ) 4. B 25(25x 3  – 4y 2 ) 5. A 6. B 8x(2x – 3y) 7.B 3a(2a – 3b) 8. B 6ab(2a – 3a 2 )...
Activity 38 Name:_______________________Score:_____________Date:_____________ Year and Section: _________________Teacher: ...
Answers 1. H 2. F 3. J 4. D 5. C 6. B 7. I 8. A 9. G 10. E Questions
Activity 39 Name: _______________________Score:_____________Date: ______________ Year and Section: _________________Teache...
Answers 1. 2(ab + 4a 2 b 2 c 2  – 8a 3 b 3 c 3 2. 2ay(5ay 2  + 2) 3. 2c(c 2  – 2c – 3) 4. 11m(1 + 2m) 5. 12a(a 2  – 2a – 4...
Activity 40 Name: _______________________Score:_____________Date:__________ Year and Section: _________________Teacher: __...
Answers 1. A 2. A 3. A 4. A 5. A 6. B (2x + y)(a - 2b)(a + 2b) 7. B (x + y + z) (x + y - z). 8. B (m + n) (x + y) (x – y) ...
Activity 41 Name:_______________________Score:_____________Date:___________ Year and Section: _________________Teacher: __...
Answers 1. C 2. J 3. E 4. H 5. B 6. G 7. F 8. A 9. D 10. I Questions
Activity 42 Name: ________________________Score:_____________ Date: _________ Year and Section: _________________Teacher: ...
Activity 43 Name: _______________________Score:_____________ Date:_______ Year and Section: _________________Teacher: ____...
Answers 1. B (m + 7) (m - 7) 2. B (bx + y) (xx – y) 3. A  4. B (8xy + x) (8xy – x) 5. A 6. A 7. A 8. A 9. A 10. A Questions
Activity 44 Name:  _______________________ Score:_____________Date: _________ Year and Section: _________________Teacher: ...
Answers 1. C 2. J 3. G 4. A 5. H 6. B 7. I 8. F 9. D 10. E Questions
Activity 45 Name: _______________________Score:_____________Date: ______________ Year and Section: _________________Teache...
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
Workbook in Solving Algebraic Expression
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Workbook in Solving Algebraic Expression

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Activities in Solving Algebraic Expression in Basic Operations, Factoring and Special Products

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Transcript of "Workbook in Solving Algebraic Expression"

  1. 1. TABLE OF CONTENTS NEXT
  2. 2. O M G PREVIOUS NEXT VISION A premier university in CALABARZON, offering academic programs and related services designed to respond to the requirements of the Philippines and the global economy, particularly in Asian Countrie s. TABLE OF CONTENTS
  3. 3. V G O PREVIOUS NEXT MISSION The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, industrial technologies, teacher education, medicine, law, arts and sciences, information technologies and other related fields. It shall also undertake research and extension services and provide progressive leadership in its areas of specialization. TABLE OF CONTENTS
  4. 4. V O M PREVIOUS NEXT GOALS In pursuit of the college vision/mission the College of Education is committed to develop the full potentials of the individuals and equip them with knowledge, skills and attitudes in Teacher Education allied fields to effectively respond to the increasing demands, challenges and opportunities of changing time for global competitiveness. TABLE OF CONTENTS
  5. 5. V G M PREVIOUS NEXT <ul><li>OBJECTIVES OF BACHELOR OF SECONDARY EDUCATION </li></ul><ul><li>  </li></ul><ul><li>Produce graduate who can demonstrate and practice the professional and ethical requirement for the Bachelor of Secondary Education such as: </li></ul><ul><li>  </li></ul><ul><li>To serve as positive and powerful role models in the pursuit of the learning thereby maintaining high regards to professional growth. </li></ul><ul><li>Focus on the significance of providing wholesome and desirable learning environment. </li></ul><ul><li>Facilitate learning process in diverse type of learners. </li></ul><ul><li>Used varied learning approaches and activities, instructional materials and learning resources. </li></ul><ul><li>Used assessment data, plan and revise teaching – learning plans. </li></ul><ul><li>Direct and strengthen the links between school and community activities. </li></ul><ul><li>Conduct research and development in Teacher Education and other related activities. </li></ul>TABLE OF CONTENTS
  6. 6. FOREWORD This Teacher’s Visual Presentation Hand-out entitled “Workbook in Solving Algebraic Expression for Second Year High School” is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Elementary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies. PREVIOUS NEXT TABLE OF CONTENTS
  7. 7. <ul><li>The students are provided with guidance and assistance of selected faculty members of the College through the selection, production and utilization of appropriate technology tools in developing technology-based teacher support materials. Through the role and functions of computers especially the Internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kind of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation of instructional materials. </li></ul><ul><li>  </li></ul><ul><li>The output of the group’s effort may serve as an educational research of the institution in providing effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students. </li></ul>PREVIOUS NEXT TABLE OF CONTENTS
  8. 8. <ul><li> FOR-IAN V. SANDOVAL </li></ul><ul><li> Computer Instructor / Adviser </li></ul><ul><li> Educational Technology 2 </li></ul><ul><li>DELIA MERCADO Module Consultant Principal of Laboratory High School </li></ul><ul><li>LYDIA R. CHAVEZ </li></ul><ul><li> Dean College of Education </li></ul>PREVIOUS NEXT TABLE OF CONTENTS
  9. 9. PREVIOUS NEXT ACKNOWLEDGEMENT The authors wish to acknowledge the following persons who gave them the inspiration and the strength to write this module: The Education Faculty of Laguna State Polytechnic University whose insights inspired the writers to finished this module; Prof. Lydia R. Chavez, Dean of College of Education for appreciating and checking our workbook. Mr. For Ian Sandoval, Module Adviser for assisting us in finishing our workbook. Mrs. Delia Mercado, Module Consultant for checking and giving pieces of advice in making our workbook. PREVIOUS NEXT TABLE OF CONTENTS
  10. 10. Dr. Corazon N. San Agustin, an Educational Technology professor for being the first one who teach us to make a module. Friends who helped to finished this module. The authors’ families who inspired them and ignited their desire to pursue their passion for writing; and Lastly, to the Lord God Almighty who is the source of enlightenment and inspiration. THE AUTHORS PREVIOUS NEXT TABLE OF CONTENTS
  11. 11. INTRODUCTION This workbook is composed of activities in understanding and analyzing different terminologies and concepts in algebraic expression, solving algebraic expression using fundamental operations, solving algebraic expression using synthetic methods, and simple types of factoring. The workbook is designed to give the learner an opportunity to develop himself in solving mathematical problems in algebra most especially in algebraic expression. The exercises in understanding and analyzing different terminologies and concepts in algebraic expression, solving algebraic expression using fundamental operations, solving algebraic expression using synthetic methods, and simple types of factoring are for the student’s self improvement. The exercises were designed to give the learner ample exercises to develop skill in solving algebraic expressions and mathematical problems in algebra. PREVIOUS NEXT TABLE OF CONTENTS
  12. 12. GENERAL OBJECTIVES In this workbook entitled “Workbook in Solving Algebraic Expression for Second Year High School Students” the students are expected to: 1. Differentiate concept and terminologies in algebraic expression. 2. Measure proficiency in analyzing the function of terminologies in algebraic expression. 3. Avoid guessing an answer in true or false. 4. Define different terminologies in algebraic expression. 5. Analyze the standards in answering fill in the blanks test. 6. Explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression. PREVIOUS NEXT TABLE OF CONTENTS
  13. 13. 7. Recognize the different terms of a polynomial. 8. Write a monomial, binomial and trinomial equation. 9. Specify if the equation is a monomial, binomial or trinomial. 10. Define different terms of polynomial. 11. Compare monomial to binomial, binomial to trinomial. 12. Improve the abilities in comparing monomial to binomial and binomial to trinomial. 13. Write different equation of a polynomial in a monomial, binomial and trinomial. 14. Identify different terms of polynomials. 15. Increased proficiency in comparing monomial, binomial and trinomial PREVIOUS NEXT TABLE OF CONTENTS
  14. 14. 16. Recall the different degree of polynomial. 17. Have confidence to their self to find the correct answer. 18. Improve the abilities in matching an equation to each degree of polynomials. 19. Identify degree of polynomials. 20. Select the best answer in identifying the degree of polynomial. 21. Have patient in answering multiple choice test. PREVIOUS NEXT TABLE OF CONTENTS
  15. 15. TABLE OF CONTENTS Vision, Mission, Goals and Objectives Foreword Acknowledgement Introduction General Objectives PREVIOUS NEXT
  16. 16. PREVIOUS NEXT Chapter I Understanding and Analyzing Different Terminologies in Algebraic Expression Pre Test I Activity 1 Activity 2 Activity 3 Activity 4 Activity 5 Activity 6 Activity 7
  17. 17. PREVIOUS NEXT Chapter II Solving Algebraic Expression Using Fundamental Operations Post Test I Activity 10 Pre Test II Activity 11 Activity 14 Activity 12 Activity 13 Activity 9 Activity 8
  18. 18. PREVIOUS NEXT Activity 18 Activity 19 Activity 20 Activity 21 Post Test II Activity 15 Activity 17 Activity 16
  19. 19. PREVIOUS NEXT Activity 24 Activity 25 Activity 26 Activity 27 Activity 28 Chapter III Using Synthetic Method in Solving Algebraic Expression Activity 23 Activity 22 Pre Test III
  20. 20. PREVIOUS NEXT Activity 32 Activity 33 Activity 34 Activity 35 Activity 36 Post Test III Activity 31 Activity 30 Activity 29
  21. 21. PREVIOUS NEXT Chapter IV Simple Types of Factoring of Algebraic Expression Pre Test IV Activity 37 Activity 38 Activity 39 Activity 40 Activity 41 Activity 42 Activity 43
  22. 22. PREVIOUS NEXT Post Test IV Activity 44 Activity 45 Activity 46 Activity 47 Activity 48 Activity 49 Activity 50 Activity 51 Activity 52 Activity 53 Activity 54
  23. 23. About the Author References PREVIOUS NEXT Final
  24. 24. Pre Test I Name: __________________________Score: _____________Date: _______________ <ul><ul><ul><ul><li>Year and Section: ____________________Teacher: ___________________________ </li></ul></ul></ul></ul><ul><li>Objectives: </li></ul><ul><li>To define the different terminologies in algebraic expression; </li></ul><ul><li>To illustrate different expressions; </li></ul><ul><li>To analyze different equations and figure out what are the characteristics of an expressions; and </li></ul><ul><li>To increase proficiency in analyzing the functions of an algebraic expressions. </li></ul>TABLE OF CONTENTS PREVIOUS NEXT A , B C , D E , F G , H I
  25. 25. <ul><li>A. Instruction: Tell whether the statements below are true or false by writing A if the statements is correct and B if the statement is incorrect. </li></ul><ul><li>__________1. Variable is any number that is used to represents any element of a given polynomial. </li></ul><ul><li>__________2. Exponent is positive or negative integer, written in the upper left of letters or symbols. </li></ul><ul><li>__________3. Numerical coefficient is a letter or symbol. </li></ul><ul><li>__________4. Literal coefficient is a number. </li></ul><ul><li>__________5. Like terms are terms which differ only in their literal coefficient. </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><li>  </li></ul>PREVIOUS NEXT ANWERS B. Instruction: Match the given symbols and numbers in column A to its corresponding concepts and terminologies in column B . A B ____1. a, b, c, x, y, z a. Algebraic Expression ____2. 2, 4, 6, 10, 20 b. Numerical ____3. 5x² + y, 6x²y + 5y c. Exponent ____4. 6x³ + 4y, the number raise on the upper right of the variable x is called____________. d. Second term ____5. 5x² - 8x + 2 e. Variables  
  26. 26. <ul><li>C. Instruction: Identify the terms and terminologies stated in each number. Write your answer in the space provided before the numbers. </li></ul><ul><li>____________1. It is a number in a given polynomials and they are real numbers in a polynomial. </li></ul><ul><li>____________2. It is a letter or symbol coefficient containing non-negative power or exponent. </li></ul><ul><li>____________3. It is a polynomial containing only one term. </li></ul><ul><li>____________4. It is any letters or symbols that are used to represents any element of a polynomial. </li></ul><ul><li>____________5. It is a combination of variables and constants which involved of finite numbers of indicated operation raise with a power and extract of square root. </li></ul>PREVIOUS NEXT ANWERS D. Instruction: Multiple Choice. Write A if the expressions is monomial B if it is binomial and C if the expressions is trinomial _____1. 7x² - 9 _____2. 4xy _____3. 6mn + 1 _____4. 86x² + 43xy + 20y _____5. 8k³ + 6s² + 4y
  27. 27. <ul><li>F. Instruction: Identify the polynomials in column A to its corresponding terms in column B . Write your answer in the space provided </li></ul><ul><li>A B </li></ul><ul><li>_____ 1. xy a. trinomial </li></ul><ul><li>_____ 2. 5x² - 8y + 2 b. binomial </li></ul><ul><li>_____ 3. 7x² + y c. monomial </li></ul><ul><li>_____ 4. Monomial d. 4ab </li></ul><ul><li>_____ 5. Trinomial e. 6v³ + 5x – 9 </li></ul><ul><li>  </li></ul>PREVIOUS NEXT ANWERS E. Instruction: Identify the terms of polynomials. Write your answer in the space provided before each number.   __________ 1. 6x² - 8 __________ 2. 5x² + 35xy + 25y² __________ 3. 9xy __________ 4. 8x² + 10x __________ 5. 7x² + 5xy + 9y²
  28. 28. <ul><li>G . Instruction: Identify the polynomial in column A to its corresponding degree in column B . Write your answer in the space provided. </li></ul><ul><li>A B </li></ul><ul><li>_____ 1. 7x³y a. 9 th degree </li></ul><ul><li>________ 2. 21a⁶b³ + 14ab² + 1 b. 7 th degree </li></ul><ul><li>________ 3. 4x² c. 4 th degree </li></ul><ul><li>________ 4. 7yz⁵ + 2x³y d. 6 st degree </li></ul><ul><li>________ 5. 16x⁶y + 4x³y² + 2y e. 2 th degree </li></ul>PREVIOUS NEXT ANWERS H. Instruction: Multiple Choice. Identify the degree of the polynomials. Encircle the correct answer.   1. 20x⁶a³ + 10x⁴a³ - a²x a. 2 nd degree b. 7 th degree c. 9 th degree   2. xyz a. 1 st degree b. 2 nd degree c. 3 rd degree   3. 8x² - 6x³y² + 4y⁵ a. 3 rd degree b. 4 th degree c. 5 th degree   4. x⁵ - y⁸ a. 6 th degree b. 7 th degree c. 8 th degree 5. 5x² + 4y⁶ a. 1 st degree b. 3 rd degree c. 6 th degree
  29. 29. <ul><li>I. Instruction: Identify the degrees of polynomials. Write your answer in the space provided. </li></ul><ul><li>  </li></ul><ul><li>__________ 1. 15x⁵a + 8x⁴a⁴ - a³x </li></ul><ul><li>__________ 2. 5x⁴y² - 7x⁵y⁴ + 13x²y⁵ </li></ul><ul><li>__________ 3. 12x³y⁸ + 24x⁶y⁴ </li></ul><ul><li>__________ 4. 16x⁴y³z² </li></ul><ul><li>__________ 5. 5x² + 4y⁶ </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><li>  </li></ul>PREVIOUS NEXT ANWERS
  30. 30. Answers QUESTIONS QUESTIONS QUESTIONS QUESTIONS A. 1.B 2.B 3.B 4.B 5.B B. 1. e 2. b 3. a 4. c 5. d C. 1. constant 2.Literal coefficient 3. monomial 4. variable 5. polynomials D . 1. B 2. A 3. B 4. C 5. C
  31. 31. QUESTIONS QUESTIONS QUESTIONS QUESTIONS QUESTIONS G . 1. c 2. a 3. e 4. d 5. b H . 1. c 2.c 3.c 4.c 5.c F . 1. binomial 2. trinomial 3. monomial 4. binomial 5. trinomial E . 1. c 2. a 3. b 4. d 5. e I. 1. 8 th degree 2. 9 th degree 3. 11 th degree 4. 9 th degree 5. 6 th degree
  32. 32. <ul><li>Activity 1 </li></ul><ul><li>Name: __________________Score:_____________Date: ____________ </li></ul><ul><li>Year and Section: _______________Teacher:______________________ </li></ul><ul><li>Objectives: </li></ul><ul><li>1. To differentiate concept and terminologies in algebraic expression. </li></ul><ul><li>To measure proficiency in analyzing the function of terminologies in algebraic expression </li></ul><ul><li>To avoid guessing an answer in true or false test. </li></ul>Instruction: Tell whether if the statements below are true or false. Write A if the statements is correct and B if the statement is incorrect. _____________1. Variable is any numbers that are used to represents any of element of a given polynomial. Previous Next TABLE OF CONTENTS _____________2. Exponent is positive or negative integer, written in the upper left of letters or symbols. _____________3. Numerical coefficient is a letter or symbol. _____________4. Like term is a term which differ only in their literal coefficient. _____________5. Polynomial is an algebraic expression involves non-negative powers. _____________6. Coefficient is the factor of product of a polynomial. _____________7. Constant is a number in a given polynomial. _____________8. Constant is a real number in a polynomial. _____________9. Numerical coefficient is constant coefficient. _____________10. Literal coefficient is a number. Answers
  33. 33. <ul><li>Answers </li></ul><ul><li>1. B </li></ul><ul><li>2. B </li></ul><ul><li>3. B </li></ul><ul><li>4. B </li></ul><ul><li>5. A </li></ul><ul><li>6. A </li></ul><ul><li>7. A </li></ul><ul><li>8. B </li></ul><ul><li>9. A </li></ul><ul><li>10. A </li></ul>Questions
  34. 34. <ul><li>Activity 2 </li></ul><ul><li>Name:__________________________Score:_____________Date:_______________ </li></ul><ul><li>Year and Section: ________________ Teacher: ______________________________ </li></ul><ul><li>  </li></ul><ul><li>Objectives: </li></ul><ul><li>To recall different terminologies in algebraic expression. </li></ul><ul><li>To compare variables, exponents, constant and coefficient. </li></ul><ul><li>To prevent guessing an answer. </li></ul>Instruction: Match the given symbols and numbers in column A to its corresponding concepts and terminologies in column B . Previous Next TABLE OF CONTENTS A B ____1. a, b, c, x, y, z a. Algebraic Expression ____2. 2, 4, 6, 10, 20 b. Like term ____3. 5x² + y, 6x²y + 5y c. First Term ____4. ² ³ ⁴ ⁵ ⁶ ⁸ d. Term ____5. 5x² - 8x + 2 e. Literal ____6. 6x², 3x², x² f. Variable ____7. 5 is _____coefficient of x,y,z g. Exponent ____8. xy is _____coefficient of 3 h. Second term ____9. 8xy + 3mn +4hk i. Constant ____10. 3x² - 6xy + y² j. Numerical Answers
  35. 35. <ul><li>Answers </li></ul><ul><li>1. f </li></ul><ul><li>2. i </li></ul><ul><li>3. a </li></ul><ul><li>4. g </li></ul><ul><li>5. d </li></ul><ul><li>6. b </li></ul><ul><li>7. j </li></ul><ul><li>8. e </li></ul><ul><li>9. c </li></ul><ul><li>10. h </li></ul>Questions
  36. 36. Activity 3 Name: _______________________Score: ___________Date:__________ Year and Section: _____________Teacher:________________________ Instruction: Identify the terms and terminologies stated in each number. Write your answer in the space provided before the numbers. <ul><li>Objectives: </li></ul><ul><li>To define different terminologies in algebraic expression. </li></ul><ul><li>To analyze the standards in answering fill in the blanks test. </li></ul><ul><li>To explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression. </li></ul>Previous Next TABLE OF CONTENTS __________1. It is a number in a given polynomials and they are real numbers in a polynomial. __________2. It is a letter or symbol coefficient containing non-negative power or exponent. __________3. It is a polynomial containing of only one term. __________4. It is any letters or symbols that are used to represents of any element of a polynomial. __________5. It is a combination of variables and constant which involved of finite numbers of indicated operation raise with a power and extract of square root.   Answers
  37. 37. Previous Next Answers __________6. It is a positive or negative integer, written in the upper right of letters or symbols. __________7. It is polynomial contains of two terms. __________8. It is a terms which differ only in their constant coefficient. __________9. It is an algebraic expression involves non-negative powers or exponents containing numbers or variables. It contains of one or more terms. __________10. It is a polynomial contains of three terms.
  38. 38. <ul><li>Answers </li></ul><ul><li>1.constant </li></ul><ul><li>2.Literal coefficient </li></ul><ul><li>3.monomial </li></ul><ul><li>4.variable </li></ul><ul><li>5.term </li></ul><ul><li>6.exponent </li></ul><ul><li>7.binomial </li></ul><ul><li>8.Like terms </li></ul><ul><li>9.polynomial </li></ul><ul><li>10.trinomial </li></ul>Questions 1 – 5 Questions 6 – 10
  39. 39. Activity 4 Name:______________________Score:_________Date:_____________ Year and Section:_________________Teacher:____________________ Instruction: Multiple Choice. Write A if the equation is monomial B if the equation is binomial and C if the equation is trinomial. <ul><li>Objectives: </li></ul><ul><li>To recognize the different terms of a polynomial. </li></ul><ul><li>To write a monomial, binomial and trinomial equation. </li></ul><ul><li>To specify if the equation is a monomial, binomial or trinomial. </li></ul>Previous Next TABLE OF CONTENTS   ___________1. 7x² - 9 ___________2. 4xy ___________3. 6mn + 1 ___________4. 86x² + 43xy + 20y ___________5. 8k³ + 6s² + 4y ___________6. 36ab ___________7. 9x² -3y + 1 ___________8. 5x³ + y² ___________9. 89xy ___________10. 25x² + y   Answers
  40. 40. <ul><li>Answers </li></ul><ul><li>1.B </li></ul><ul><li>2.A </li></ul><ul><li>3.B </li></ul><ul><li>4.C </li></ul><ul><li>5.C </li></ul><ul><li>6.A </li></ul><ul><li>7.C </li></ul><ul><li>8.B </li></ul><ul><li>9.A </li></ul><ul><li>10.B </li></ul>Questions
  41. 41. Activity 5 Name: ______________________Score:_________Date:___________ Year and Section:________________ Teacher: __________________ Instruction: Identify the polynomials in column A to its corresponding terms in column B . Write your answer in the space provided. <ul><li>Objectives: </li></ul><ul><li>To define different terms of polynomial. </li></ul><ul><li>To compare monomial to binomial, binomial to trinomial. </li></ul><ul><li>To write different equation of a polynomial in a monomial, binomial and trinomial. </li></ul>Previous Next TABLE OF CONTENTS <ul><ul><ul><ul><li>A B </li></ul></ul></ul></ul><ul><li>____1. xy a. trinomial </li></ul><ul><li>____2. 5x² - 8y + 2 b. three </li></ul><ul><li>____3. 7x² + y c. 4m + 8l </li></ul><ul><li>____4. Monomial d. two </li></ul><ul><li>____5. Binomial e. monomial </li></ul><ul><li>____6. Trinomial f. one </li></ul><ul><li>____7. Monomial contains _______ term g. polynomial </li></ul><ul><li>____8. Binomial contains ________ terms h. 4ab </li></ul><ul><li>____9. Monomial, binomial, trinomial i. 6v³ + 5x – 9 </li></ul><ul><li>____10. Trinomial contains________ terms j. binomial </li></ul>Answers
  42. 42. <ul><li>Answers </li></ul><ul><li>1.e </li></ul><ul><li>2.a </li></ul><ul><li>3.j </li></ul><ul><li>4.h </li></ul><ul><li>5.c </li></ul><ul><li>6.i </li></ul><ul><li>7.f </li></ul><ul><li>8.d </li></ul><ul><li>9.g </li></ul><ul><li>10.b </li></ul>Questions
  43. 43. Activity 6 Name:____________________Score:_____________Date:____________ Year and Section:____________________Teacher: ___________________ Objectives: 1. To identify different terms of polynomials; 2. To increase proficiency in comparing monomial, binomial and trinomial; and 3. To improve the abilities in comparing monomial to binomial and binomial to trinomial. Instruction: Identify the number of terms of the given polynomials. Write your answer in the space provided before each number. ______________1. 6x² - 8 ______________2. 5x² + 35xy + 25y² ______________3. 9xy ______________4. 8x² + 10x ______________5. 7x² + 5xy + 9y² ______________6. 25xy + 14y ______________7. 10ab ______________8. 81x² + 6xy – 14y ______________9. 49x² + 16y² ______________10. 36a² - 25b⁴     Previous Next Answers TABLE OF CONTENTS
  44. 44. Answers <ul><li>1.binomial </li></ul><ul><li>2.trinomial </li></ul><ul><li>3.monomial </li></ul><ul><li>4.binomial </li></ul><ul><li>5.trinomial </li></ul><ul><li>6.binomial </li></ul><ul><li>7.monomial </li></ul><ul><li>8.trinomial </li></ul><ul><li>9.binomial </li></ul><ul><li>10.binomial </li></ul>Questions
  45. 45. Activity 7 Name: ________________________Score:_____________Date:_____________ Year and Section:___________________Teacher: ________________________ Instruction: Match the polynomial in column A to its corresponding degree in column B . Write your answer in the space provided. A B __________1. 7x³y a. 4 th degree __________2. 21a⁶b³ + 14ab² + 1 b. 6 th degree __________3. 4x² c. 8 th degree __________4. 7yz⁵ + 2x³y d. 1 st degree __________5. 16x⁵y + 4x³y² + 2y e. 7 th degree __________6. 3x f. 0 degree __________7. 3 + 5 g. 2 nd degree __________8. 7m⁶n² + 3mn² + 1 j. 3 rd degree __________9. 16x⁴y³ + 3y² i. 9 th degree __________10. 5x³ h. 5 th degree <ul><li>Objectives: </li></ul><ul><li>To recall the different degrees of polynomial; </li></ul><ul><li>To have self confidence in finding the correct answers; and </li></ul><ul><li>To improve the abilities in matching an expressions to each degrees of polynomials. </li></ul>Previous Next Answers TABLE OF CONTENTS
  46. 46. Answers <ul><li>1.a </li></ul><ul><li>2.i </li></ul><ul><li>3.g </li></ul><ul><li>4.h </li></ul><ul><li>5.b </li></ul><ul><li>6.d </li></ul><ul><li>7.f </li></ul><ul><li>8.j </li></ul><ul><li>9.e </li></ul><ul><li>10.c </li></ul>Questions
  47. 47. Activity 8 Name:_______________________Score:_____________Date:____________ Year and Section:____________________Teacher:_____________________ Instruction: Identify the degree of the polynomials. Encircle the correct answer. 1. 20x⁶a³ + 10x⁴a³ - a²x a. 2 nd degree b. 7 th degree c. 9 th degree 2. 2xyz a. 1 st degree b. 2 nd degree c. 3 rd degree 3. 8x² - 6x³y² + 4y⁵ a. 3 rd degree b. 4 th degree c. 5 th degree <ul><li>Objectives: </li></ul><ul><li>To identify degree of polynomials. </li></ul><ul><li>To select the best answer in identifying the degree of polynomial. </li></ul><ul><li>To have patient in answering multiple choice test. </li></ul>Previous Next Answers TABLE OF CONTENTS
  48. 48. <ul><li>4 . x⁵ - y⁸ </li></ul><ul><li> a. 6 th degree b. 7 th degree c. 8 th degree </li></ul><ul><li>5. 5x² + 4y⁶ </li></ul><ul><li> a. 1 st degree b. 3 rd degree c. 6 th degree </li></ul><ul><li>  6. 12x³y⁸ + 6x⁶y⁴ </li></ul><ul><li> a. 11 th degree b. 10 th degree c. 9 th degree </li></ul><ul><li>7. 5x⁴y³z² </li></ul><ul><li>a. 9 th degree b. 8 th degree c. 7 th degree </li></ul><ul><li>8. 6a³ + a²b⁴ + 12a²b² + 38b⁴ </li></ul><ul><li> a. 5 th degree b. 6 th degree c. 7 th degree </li></ul><ul><li>9. xyz </li></ul><ul><li> a. 1 st degree b. 2 nd degree c. 3 rd degree </li></ul><ul><li>  </li></ul><ul><li>10. x⁶-y³ </li></ul><ul><li> a. 7 th degree b. 8 th degree c. 9 th degree </li></ul><ul><li>  </li></ul><ul><li>  </li></ul>Previous Next Answers
  49. 49. Answers <ul><li>1.c </li></ul><ul><li>2.c </li></ul><ul><li>3.c </li></ul><ul><li>4.c </li></ul><ul><li>5.c </li></ul><ul><li>6.a </li></ul><ul><li>7. a </li></ul><ul><li>8.b </li></ul><ul><li>9.c </li></ul><ul><li>10.a </li></ul>Questions 1 - 3 Questions 4 - 10
  50. 50. <ul><li>Instruction: Identify the degree of the given polynomials. Write your answer in the space provided. </li></ul><ul><li>_________1. 15x⁵a + 8x⁴a⁴ - a³x </li></ul><ul><li>_________2. 5x⁴y² - 7x⁵y⁴ + 13x²y⁵ </li></ul><ul><li>_________3. 12x³y⁸ + 24x⁶y⁴ </li></ul><ul><li>_________4. 16x⁴y³z² </li></ul><ul><li>_________5. 5x² + 4y⁶ </li></ul><ul><li>_________6. 3a²b²c⁶+ 4a²b⁴c⁶ + 2a²b⁶c⁸ </li></ul><ul><li>_________7. 24xyz </li></ul><ul><li>_________8. 8x² - 7x³y² +6y⁵ </li></ul><ul><li>_________9. 2a³ + a²b⁴ + 13a²b² + 38b⁴ </li></ul><ul><li>_________10. x⁵ - y⁸ </li></ul><ul><li>  </li></ul>Activity 9 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To identify the degree of polynomials; </li></ul><ul><li>To write the answers correctly; and </li></ul><ul><li>To have patience in identifying the degree of polynomials. </li></ul>Previous Next Answers TABLE OF CONTENTS
  51. 51. Answers <ul><li>1.8 th degree </li></ul><ul><li>2.9 th degree </li></ul><ul><li>3.11 th degree </li></ul><ul><li>4.9 th degree </li></ul><ul><li>5.6 th degree </li></ul><ul><li>6.16 th degree </li></ul><ul><li>7.3 th degree </li></ul><ul><li>8.5 th degree </li></ul><ul><li>9.6 th degree </li></ul><ul><li>10.8 th degree </li></ul>Questions
  52. 52. Post Test I Name:__________________________Score:_____________Date:_______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To define the different terminologies in algebraic expression; </li></ul><ul><li>To illustrate different expressions; </li></ul><ul><li>To analyze different expressions and figure out what are the characteristics of this expression; and </li></ul><ul><li>To increase proficiency in analyzing the functions of an algebraic expressions. </li></ul>Previous Next TABLE OF CONTENTS B C A D
  53. 53. A. Instruction: Identify the terms and terminologies in each number. Encircle the letter of your answer.   1. It is a letter or symbol coefficient containing nonnegative power or exponent. a. Terms b. Coefficient c. Exponent 2. It is any letter or symbol that is used to represent any element of a given polynomial. a. Algebraic Expression b. Variables c. Polynomials 3. It is a positive or negative integer, written in the upper right of letters any or symbols.   a. Exponent b. Integers c. Monomial 4. Terms which differ only in their constant coefficient is called___________. a. Coefficient b. Literal Coefficient c. Like Terms 5. It is a polynomial containing three terms. a. Monomial b. Binomial c. Trinomial   Previous Next Answers
  54. 54. 6. It is a number in a given polynomial. a. Constant b. Variable c. Exponent 7. Algebraic Expression involves non-negative power or exponent containing numbers or variables.   a. Polynomial b. Numerical Coefficient c. Literal Coefficient   8. It is a number or a constant with variables and containing non-negative powers or exponents.   a. Coefficient b. Polynomial c. Variable 9. It is a factor of product of a polynomial. a. Terms b. Degree c. Factor 10. It is a polynomial contains one term. a. Monomial b. Binomial c. Trinomial   Previous Next Answers
  55. 55. <ul><li>B. Identify the terms of the polynomials. Write R if the given polynomial is monomial, M if the given polynomial is binomial and E if it is trinomial. </li></ul><ul><li>______11. 4x² - 1 </li></ul><ul><li>_____12. 9x² + 25xy + 16y² </li></ul><ul><li>_____13. 4xy </li></ul><ul><li>_____14. 3x² + 7x </li></ul><ul><li>_____15. x² +2xy + y² </li></ul><ul><li>_____16. -6xy + 14y </li></ul><ul><li>_____17. 8ab </li></ul><ul><li>_____18. 3x² - 6xy -14y </li></ul><ul><li>_____19. 9x² + 16y² </li></ul><ul><li>_____20. 25a⁴ - 36b⁸ </li></ul><ul><li>_____21. 4rt </li></ul><ul><li>_____22. 5c + k </li></ul><ul><li>_____23. 5x² - 8x + 2 </li></ul><ul><li>_____24. 3y³ </li></ul><ul><li>_____25. 4x³ + 8y² </li></ul>Previous Next Answers
  56. 56. <ul><li>C. Identify the degree of polynomials. Write your answer in the space provided. </li></ul><ul><li>  </li></ul><ul><li>__________26. 15x³a + 8x²a² - a³x </li></ul><ul><li>__________27. 5x⁴y³ - 7x⁵y³ + 13x⁶y⁵ </li></ul><ul><li>__________28. 12x³y³ + 24x²y⁴ </li></ul><ul><li>__________29. 16x³y²z </li></ul><ul><li>__________30. 5x² + 4y </li></ul><ul><li>__________31. 3a²b²c⁶+ 4a²b⁴c⁶ + 2a²b⁶c⁸ </li></ul><ul><li>__________32. 24xyz </li></ul><ul><li>__________33. 8x² - 7xy +6y </li></ul><ul><li>__________34. 2a³ + a²b + 13ab² + 38b⁴ </li></ul><ul><li>__________35. x⁵ - y </li></ul><ul><li>__________36.3x³ </li></ul><ul><li>__________37. 7x²y⁵ </li></ul><ul><li>__________38. 16x⁵y + 4x³y² + 2y </li></ul><ul><li>__________39. 7m⁶ + 4x -5y </li></ul><ul><li>__________40. 3x + 6 </li></ul>Previous Next Answers
  57. 57. <ul><li>D. True or False. Write E if the statement is correct and R if the statement is incorrect. Write your answer in the space provided. </li></ul><ul><li>  </li></ul><ul><li>_____1. Algebraic expression is a combination of variables and constants which involved finite numbers. </li></ul><ul><li>_____2. In 9x², 2 is the exponent of x. </li></ul><ul><li>_____3. In 5x² - 8x + 2, 5x² is in the 1 st term. </li></ul><ul><li>_____4. 4rt is a monomial </li></ul><ul><li>_____5. In 7x²y⁵, the degree of a monomial is in the 5 th degree. </li></ul><ul><li>_____6. In 4x³y², 4 is a numerical coefficient. </li></ul><ul><li>_____7. 5x² - 8x + 2 is a trinomial. </li></ul><ul><li>_____8. In 5xyz, 5x is coefficient of yz. </li></ul><ul><li>_____9. In 16x⁵y + 4x²y² + 2y, the degree of a trinomial is in 7 th degree. </li></ul><ul><li>_____10. In 45c⁵g², c⁵g² is the literal coefficients </li></ul>Previous Next Answers
  58. 58. Answers <ul><li>A. </li></ul><ul><li>1.a </li></ul><ul><li>2.b </li></ul><ul><li>3.a </li></ul><ul><li>4.c </li></ul><ul><li>5.c </li></ul><ul><li>6.a </li></ul><ul><li>7.a </li></ul><ul><li>8.a </li></ul><ul><li>9.a </li></ul><ul><li>10.a </li></ul>Questions D Questions C Questions B Questions A B. 11.M 12.E 13.R 14.M 15.E 16.M 17.R 18.E 19.M 20.M 21.R 22.M 23.E 24.R 25.M C. 26. 4 th degree 27. 11 th degree 28. 6 th degree 29. 6 th degree 30. 2 nd degree 31. 16 th degree 32. 3 rd degree 33. 2 nd degree 34. 4 th degree 35. 5 th degree 36. 3 rd degree 37. 7 th degree 38. 6 th degree 39. 6 th degree 40. 1 st degree D. 1.E 2E. 3.E 4.E 5.R 6.E 7.E 8.E 9.R 10.E
  59. 59. Pre Test II Name:__________________________Score:_____________ Date:____________ Year and Section:__________________Teacher: __________________________ Previous Next TABLE OF CONTENTS <ul><li>Objectives: </li></ul><ul><li>To enhance the student’s skill in solving the algebraic expression using fundamentals operation; </li></ul><ul><li>To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations; and </li></ul><ul><li>To have more practice in solving polynomials. </li></ul>
  60. 60. INSTRUCTION: Write your solution in performing the given operations. 1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c) 2. (3x – 8y + 6z) + ( 7y – 2x + 4z) 3. (5x³ + 2y²) + ( 7x³ - y²) 4. (6 – y + 3x) + (-8x + 2y + 10) 5. (7x + 4y) + (5x + 8y) 6. (5x² + 4y) + (7x² + 5y) 7. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y) 8. (3x + 4xy – 6y) + (4xy – 3y + 2x) 9. (8x⁵ - 3xy³ + 2y²) + (2x⁵ - 2xy³ + 2y²) 10. (5a² + 3ab + 6c) + (8a² + 3ab + 4c)   Previous Next Solutions
  61. 61. 11. (-5x² – 4x + 2y) – (6x² - x + 3)   12. (2a³ + a² + 4a – 3) – (4a³ - 8a² + 2a + 6)   13. (16a + 9b) – (8a + 2b)   14. (-16a + 9b) – (8a – 7b)   15. (x³ - 3x² + 7x + 2) – (5x³ + x² - 10x + 24)   16. (x + y)(2x + 3y)(5x + 4y)   17. (2m 2 )(4m)   18. 3x 3 (4y 2 )   19. (5a + 7b – 8c)(8a + 4c)   20. (9u + 5v – 2z)(5u + 2v – 2u) Previous Next Solutions
  62. 62. 21. (88x – 44y) + (55x + 22y)   22. (37b + 49ab² - 28a³) + ( 34a³ - 32ab² - 25b)   23. (59x² + 49y) + (74x² + 54y)   24. 13x(85z)   25. (73x + 45xy – 66y) + (64xy – 93y + 82x)   26. 34m²p(86op)   27. (13x³ +14y + 24xy²) + (32x³ + 84xy² + 26y)   28. 18j²(17j⁸k⁶)   29. 14h²l⁵(-36t²)   30. 59i⁶l²(61u³v³) Previous Next Solutions
  63. 63. 31. 58xyz(34xz)   32. -14f²(62huv)   33. 28xy²(18x²)   34. 92a²b²c(57a³b²c²)   35. (x 2 + 7x + 10) ÷ (x – 5)   36. (2 3 a 4 b) ÷ (3 2 c)   37. (x 2 – 9x – 10) ÷ (x + 1)   38. (a 3 – 1)(a – 1)   39. (12t 4 – 25t 3 + 18t 2 + 7t – 25) ÷ (3t – 4)   40. (73x + 45xy – 66y) + (64xy – 93y + 82x)   Previous Next Solutions
  64. 64. Answers Pre Test 31 - 40 Pre Test 21 - 30 Pre Test 11-20 Pre Test 1 - 10 A. 1. 14a 2 – 10b + 5c 2. x – y + 10z 3. 12x 3 + y 2 4. -5x + y + 16 5. 12x + 12y 6. 12x 2 + 9y 7. 6x 3 + 12xy 2 + 6y 8.5x + 8xy – 9y 9. 10x 5 + 5xy 3 + 4y 2 10.13a 2 + 6ab + 10c B 11.-11x 2 – 3x + 2y + 3 12. -2a 3 – 7a 2 + 6a + 3 13. 8a + 7b 14. -24a + 16b 15. -4x 3 – 4x 2 + 17x + 22 16. 10x 3 + 33x 2 y + 35xy 2 + 12y 3 17. 8m 3 18. 12x 3 y 2 19. 40a 2 + 56ab – 44ac + 28bc – 32c 2 20. 27u 2 + 33uv – 6uz + 10v 2 – 4vz C 21. 113x – 22y 22. 6a 3 + 7ab 2 + 12b 23. 133x 2 + 103y 24. 1105xz 25. 155x + 109xy – 159y 26. 2924 m 2 op 2 27.45x 3 + 40y + 108xyz 28.306j 10 k 6 29. -504h 2 l 5 t 2 30.3599i 6 l 3 u 3 v 3 D 31. 1972 x 2 yz 2 32. -868 f 2 huv 33. 504x 3 y 2 34. 5244a 5 b 4 c 3 35. x + 10 r. 70 36. 8a 4 b/9C 37. x – 10 38. a 4 – a 3 – a + 1 39. 4t 3 – 3t 2 + 2t + 5 r. -5 40. 155x + 109xy – 159
  65. 65. Activity 10 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to add polynomials; </li></ul><ul><li>To help the students to enhance their skills in adding two or more polynomials; and </li></ul><ul><li>To measure the capacity of the students in choosing the correct answer. </li></ul>INSTRUCTION: Choose the best answer in the box and write the letter on the space provided before the number.   a. 12x 3 - y 2 f. 5x + y + 16 k. 6a + 3ab + 4c p. x – y + 10z b. 12x – 12y g. –a + 3b l. 12x 3 + y 2 q. 12x + 12y c. 21x – 8xy + y h. 7x – 10y + 8z m. 21x + 8xy + y r. 7x + 10y + 8z d. 14a 2 + 10b + 5c i. 7x – 2y + 4 n. 6a – 3ab + 4c s. 14a 2 - 10b + 5c e. –x + y +10z j. a + 3b o. 7x + 2y + 4 t. -5x + y + 16           Previous Next TABLE OF CONTENTS
  66. 66.   _____1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c) _____2. (3x – 8y + 6z) + ( 7y – 2x + 4z) _____3. (5x³ + 2y²) + ( 7x³ - y²) _____4. (6 – y + 3x) + (-8x + 2y + 10) _____5. (7x + 4y) + (5x + 8y) _____6. (8x + 7xy + 3y) + (6x – 3xy + 4y) + (7x + 4xy – 6y) _____7. (4x + 6y + 6) + (3x – 4y – 2) _____8. (4x – 6y + 6z) + (3x – 4y +2z) _____9. (2a + ab + c) + (3c + 4a + 2ab) _____10. (2a + 4b) + ( 3a – 5b ) + ( -6a + 4b)     Previous Next Answers
  67. 67. Answers Questions 1. s 2. p 3. l 4. t 5. q 6. m 7. o 8. h 9. k 10. g
  68. 68. Activity 11 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To help the students to enhance their skills in adding two or more polynomials; </li></ul><ul><li>To make the students solve patiently; and </li></ul><ul><li>To show their solution clearly. </li></ul>INSTRUCTION: Write your solutions in performing the given conditions.   1. (8a² + 6ab – 2c) + (4a – 4ab + c) + (-2a + 6ab – 3c)   2. (6x² + 4xy – 8y) + (x² + xy + y)     3. (4a³ - 7ab² - 3c) + (7a³ + 6ab² + 2c)   4. (2a – ab – b) + (-3b – 4ab – 3a) + (-6b + 2ab + 4a)   5. (8x – 4y) + (5x + 2y)     Previous Next TABLE OF CONTENTS Answers
  69. 69. 6. (3b + 4ab² - 2a³) + ( 3a³ - 3ab² - 2b)   7. (5x² + 4y) + (7x² + 5y)   8. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y)   9. (3x + 4xy – 6y) + (4xy – 3y + 2x)   10. (8x⁵ - 3xy³ + 2y²) + (2x⁵ - 2xy³ + 2y²)   11. (5a² + 3ab + 6c) + (8a² + 3ab + 4c)   12. (6a³ + 4ab² - 8c) + (-8c +7a³ + ab²)   13. (3m + 25n – 8) ­+ (6n – 8 + 8m)   14. (8a + 7b) + (2a + 2c) + (5c – d)   15(5x + 2z) + (-2z + 5x) Previous Next Answers
  70. 70. Answers Questions 1- 5 Questions 6 - 15 1. 8a 2 + 8ab – 4c 2. 7x 2 + 5xy – 7y 3. 11a 3 – ab 2 – c 4. 3a – 3ab – 10b 5. 13x – 2y 6. a 3 + ab 2 + b 7. 12x 2 + 9y 8. 6x 3 + 12xy 2 +6y 9. 8xy – 2y 10. 10x 5 – 5xy 3 + 4y 2 11. 13a 2 + 6ab + 10c 12. 13a 3 + 5ab 2 – 16c 13. 11m + 31n - 16 14. 10a + 7b + 7c – d 15. 10x
  71. 71. Activity 12 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To have more practice in adding polynomials; </li></ul><ul><li>To enhance the students’ ability in evaluating expression; and </li></ul><ul><li>To practice the students in subtracting polynomials mentally. </li></ul>INSTRUCTION: Fill in the blanks to make the statement correct.   1. (9y 2 + 2x – 3y) + ___________________ = 11y 2 – 5x + y 2. (11t + 3x – 4u) + (-8x + 2u + 2t) = ___________________ 3. (6a 3 + 4ab 2 – 8c) + ___________________ = 13a 3 + 5ab 2 – 16c 4. (8a 2 + 3ab – 4c) + ____________________ = 2a 2 + 7ab – 6c 5. _______________ + (-4a + 5x) = -6a + 7x 6. (5t 2 + 2t – 3y) + __________________+ ________________ = 29t 2 - 4t + y 7. _______________ + (-4a 3 + 3b 2 – 4c) + _________________ = -12a 3 – 14b 2 + 8 8. _________________ + __________________ + (11j e + 18r 2 – 25x 3 ) = -15j e + 2r 2 – 5x 3 9. _________________ + (8g 3 – 6) + (g 3 + 5) = 5g 3 - 11 10.__________________ + __________________ = 11h 3 – 8x Answers Previous Next TABLE OF CONTENTS
  72. 72. Answers Questions 1. 2y 2 – 7x + 4y 2. 13t – 5x – 2u 3. 7a 3 + ab 2 – 8c 4. -6a + 4ab – 2c 5. -2a + 2x 6. 12t 2 + 2t – y and 12t 2 – 8t + 5y 7. -4a 3 – 12b 2 – 2c and -4a 3 – 5b 2 - 2c 8. -20j e – 8r 2 + 10x 3 and -6j e – 8r 2 + 10x 3 9. -4g 3 + 12 10. 5h 3 – 4x and 6h 3 -4x
  73. 73. Activity 13 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To help the students to enhance their skills in subtracting two or more polynomials; </li></ul><ul><li>To become more efficient in subtracting polynomials; and </li></ul><ul><li>To show clearly their own solution. </li></ul><ul><li>INSTRUCTION: Perform the indicated operation and show your solution. </li></ul><ul><li>  </li></ul><ul><li>Subtract 4x² - 5x + 7 to x – 8 </li></ul><ul><li>Subtract 3a² - 4a + 3 to a + 5 </li></ul><ul><li>Subtract 4a – 8b + 3c to 12a + 6b – 4c </li></ul><ul><li>(2a + 2b + 2c) – (6a – 3b + c) </li></ul><ul><li>(-5x² – 4x + 2y) – (6x² - x + 3) </li></ul><ul><li>(2a³ + a² + 4a – 3) – (4a³ - 8a² + 2a + 6) </li></ul><ul><li>(16a + 9b) – (8a + 2b) </li></ul><ul><li>(-16a + 9b) – (8a – 7b) </li></ul><ul><li>(x³ - 3x² + 7x + 2) – (5x³ + x² - 10x + 24) </li></ul><ul><li>(3x 4 +4x 3 -5x 2 +18) - (7x 5 +3x 4 -12x 3 -3x 2 + 7x - 9) </li></ul><ul><li>  </li></ul><ul><li>  </li></ul>Previous Next TABLE OF CONTENTS Answers
  74. 74. Answers Questions 1. 4x 2 – 6x + 15 2. 3a 2 – 5a – 2 3. -8a – 14b + 7c 4. -4a + 5b + c 5. -11x 2 – 3x + 2y – 3 6. -2a 3 + 7a 2 + 2a – 9 7. 8a + 7b 8. -24a + 16b 9. -4x 3 – 4x 2 + 17x – 22 10. -7x 5 + 16x 3 – 2x 2 + 27
  75. 75. Activity 14 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To help the students to enhance their skills in subtracting two or more polynomials; </li></ul><ul><li>To avoid guessing the answer; and </li></ul><ul><li>To make the students read the instruction clearly and thoroughly. </li></ul>INSTRUCTION: Draw a positive sign if the statement is correct and negative sign if the statement is incorrect in the space provided.   ___________ 1. (3x + 2y + 2z) – (6x – 5y + 3z) is equal to -3x + 7y + z. ___________ 2. In equation, (7x³ +2y² + 2z) – (-5x³ + 4y² - 6z) the second term of each polynomials have the difference of -2y 2 . ___________ 3. (3x – 9y + 4z) – (-3x – 6y + 9z) is equal to 6x – 3y -5z. ___________ 4. In (9x⁶ + 6y⁵) – (3x⁶ - 5y⁵) the exponent of the difference is in the fifth degree. ___________ 5. (9a + 7b + 4c) – (8a + 7b + 2c) is equal to a +2c. Previous Next TABLE OF CONTENTS Answers
  76. 76. ___________ 6. (-5x + 7y – z) – (6x – 7y + 2z) is equal to 11x + 14y – 3z. ___________ 7. In equation (-11x³ - 5x² - 7x -6) – (-9x³ - 6x² + 9x + 3) the third term is16x. ___________ 8. The difference of 16xy – 7xy is 9xy. ___________ 9. In (-4x³ + 6y² - 3z) – (-5x³ - 3y² - 2z), the second equation will become positive. ___________ 10.The difference of 3ab – 7ab is a positive.   Answers Previous Next
  77. 77. Answers Questions 1 - 5 Questions 6 - 10 1. + 2. + 3. + 4. - 5. + 6. - 7. + 8. + 9. + 10. -
  78. 78. Activity 15 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To make the students think fast; </li></ul><ul><li>To help the students elaborate the expressions of a polynomials; and </li></ul><ul><li>To enhance their skills in subtracting polynomials. </li></ul><ul><li>INSTRUCTION: Fill in the blanks to make the statement correct. </li></ul><ul><li>  </li></ul><ul><li>(9l 2 + 4m – 9y) - _____________ = 10l 2 – 5m + y </li></ul><ul><li>(4t + 3x – 4u) - (-5x + 2u + 2t) = _________________ </li></ul><ul><li>(6a 3 + 4ab 2 – 8c) - _________________ = 3a 3 + 5ab 2 – 16c </li></ul><ul><li>(8a 2 + 3ab – 4c) - _________________ = 2a 2 + 4ab – 6c </li></ul><ul><li>_________________ - (-4a + 5x) = -6a + 7x </li></ul><ul><li>(5t 2 + 2t – 3y) + _________________ = 29t 2 - 4t + y </li></ul><ul><li>_________________ - (-4a 3 + 3b 2 – 4c) = -12a 3 – 14b 2 + 8 </li></ul><ul><li>_________________ - _________________ = -15j e + 2r 2 – 5x 3 </li></ul><ul><li>_________________ - (8g 3 – 6) - (g 3 + 5) = 5g 3 – 11 </li></ul><ul><li>______________- _______________= 11h 3 – 8x </li></ul><ul><li>  </li></ul>Previous Next TABLE OF CONTENTS Answers
  79. 79. Answers Questions 1. –l 2 + 9m + 10y 2. 8x + 2t – 6u 3. 3a 3 – ab 2 + 8c 4. 6a 2 – ab + 2c 5. -10a + 12x 6. 24t 2 – 6t + 4y 7. -16a 3 – 11b 2 + 4c 8. 15j e + 3r 2 – 2x 3 and 30j e + r 2 + 3x 3 9. 12g 3 + 10 10. 16h 3 – 3x and 5h 3 + 5x
  80. 80. Activity 16 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To be more efficient in multiplying monomials; </li></ul><ul><li>To help the students to enhance their skills in multiplying monomials; and </li></ul><ul><li>To recall different laws in multiplying monomials. </li></ul>INSTRUCTION: Write your solutions in performing the given operations.   1. (4xy - 2)(5y – 3z 2 ) 2. -3a(3a⁴b³c²d + 3b) 3. (-4b-c)(3c + 8) 4. 2x(3x³) 5. 8u(2u³v²w) 6. (x + y)(2x + 3y)(5x + 4y) 7. (2m 2 )(4m)             Previous Next TABLE OF CONTENTS Answers
  81. 81. 8. 3x 3 (4y 2 ) 9. (5a + 7b – 8c)(8a + 4c) 10. (9u + 5v – 2z)(5u + 2v – 2u) 11. (-5x 2 y 3 w)(2x + y)   12. (4x + 2y)(5x 3 + 2x 2 – y)   13. (6a 3 + b 2 )(4a 3 + b – y)   14. (2t 2 + 3t)(4t 2 ­ – 3t 2 –t)   15. (4x 2 – y 3 )( 4x 3 – y 2 + 6)           Previous Next Answers
  82. 82. Answers Questions 1 - 7 Questions 8- 15 1. 20xy 2 – 10y – 8xyz 2 – 6z 2 2. -9a 5 b 3 cd 2 – 9ab 3. -12bc – 3c 2 – 32b – 8c 4. 6x 4 5. 16u 2 v 2 w 6. 10x 3 + 35x 2 y + 35xy 2 + 12y 3 7. 8m 3 8. 12x 3 y 2 9. 40a 2 + 56ab – 44ac + 28bc – 32c 2 10. 27u 2 + 33uv – 6uz +10x 2 – 4vz 11. -10x 3 y 3 w – 5x 2 y 2 w 12. 20x 4 + 8x 3 – 4xy + 10x 3 y + 4x 2 y – 2y 2 13. 24a 5 + 6a 3 b – 6a 3 y + 4a 3 b + b 3 – b 2 y 14. 4t 4 + t 3 -3t 2 15. 16x 5 – 4x 2 y + 24x 2 – 4x 3 y 3 + y 5 – 6y 3
  83. 83. Activity 17 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To have more attention in doing activity; </li></ul><ul><li>To make the students enjoy answering the puzzle; and </li></ul><ul><li>To enhance their skills in multiplying monomials. </li></ul>INSTRUCTION: Solve the cross-word puzzle by performing the indicated operations in the given expressions and show your solutions in the given box.   1. 2. 3. 4. 7. 5. 6. 8. 9. Previous Next TABLE OF CONTENTS Answers
  84. 84.     Across 1. (2xy)(9x²)(7y) 4. (5u²)(5u) 5. (9w)(5) 7. (zmn)(z³m²n) 8 (3x²)(3x²y) 9. (26a²)(2a²)   Down 1. (6u²)(3u) 2. 2(19)(3) 3. (yzw)(yz) 4. 2m³z² (m²z²) 6. 2(7)(3) 8. 3a²(8a)(4a) Previous Next
  85. 85. Answers Questions Across 1. 126x 3 y 2 4. 25u 3 5. 45w 7. z 4 m 3 n 2 8. 9x 4 y 9. 52a 2 Down 1. 18u 3 2. 114 3. y 2 z 2 w 4. 2m 4 z 4 6. 42 8. 96a 4
  86. 86. Activity 18 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To enhance their thinking in multiplying monomials mentally; </li></ul><ul><li>To avoid guessing the answer; and </li></ul><ul><li>To make the students more accurate their answers. </li></ul>INSTRUCTION: Match column A with column B. Write the correct letter before the number .   A B _____1. 3x²(15xy) a1. 16x 3 y 2 _____2. 4c² (2t) a7. 7uvxyz _____3. 19x(3xy) a3. -24h 2 l 5 t 2 _____4. m²p(op) a4.45x 3 y _____5. 3x(5z) b5.20x 2 yz 2 _____6. 8j²(j⁸k⁶) b2. 14a 5 b 4 c 3 _____7. 4h²l⁵(-6t²) b6. 140xyz Previous Next TABLE OF CONTENTS Answers
  87. 87. <ul><li>_____8. 9i⁶l²(6u³v³) c5. 8c 2 t </li></ul><ul><li>_____9. 5xyz (4xz) c6. m 2 op 2 </li></ul><ul><li>_____10. -14f²(6huv) d1. 8j 10 k 6 </li></ul><ul><li>_____11. 2xy² (8x²) d2. -84f 2 huv </li></ul><ul><li>_____12. 2a²b²c (7a³b²c²) e8.288c 3 n 2 </li></ul><ul><li>_____13. 5x (4y)(7z) f7. 57x 2 y </li></ul><ul><li>_____14. 7uv (xyz) g5.54 i 6 l 2 u³v³ </li></ul><ul><li>_____15. 24c (-12n²)(-c²) h8. 15 </li></ul>Previous Next Answers
  88. 88. Answers Questions 1 - 7 Questions 8 - 15 1. a4 2. c5 3. f7 4. c6 5. h8 6. d1 7. a3 8. g5 9. b5 10. d2 11. a1 12. b2 13. b6 14. a7 15. e8
  89. 89. Activity 19 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to divide polynomials. </li></ul><ul><li>To enhance the students’ skill in dividing polynomials. </li></ul><ul><li>To be more patient in dividing polynomials. </li></ul><ul><li>INSTRUCTION: Divide the following polynomials. Show your solution and encircle your answer. </li></ul><ul><li>  </li></ul><ul><li>(x²-25) ÷ (x+5) </li></ul><ul><li>(6y² + y – 5) ÷ (6y-5) </li></ul><ul><li>4 a²b² ÷ a²b² </li></ul><ul><li>(x 4 – 3x 2 + 2x) ÷ (x-1) </li></ul><ul><li>(x 2 + 7x + 10) ÷ (x – 5)   </li></ul><ul><li>(2 3 a 4 b) ÷ (3 2 c) </li></ul><ul><li>(x 2 – 9x – 10) ÷ (x + 1) </li></ul><ul><li>(a 3 – 1)(a – 1) </li></ul><ul><li>(12t 4 – 25t 3 + 18t 2 + 7t – 25) ÷ (3t – 4) </li></ul><ul><li>(56v 2 ­­­ - 5x 2 - 27vx) ÷ (7v + x) </li></ul>Previous Next TABLE OF CONTENTS Answers
  90. 90. Answers Questions 1. x – 5 2. y + 1 3. 4 4. x 5. X + 12 r. 70 6. 8a 4 b/9c 7. x – 10 8. a + 1 9. 4t 3 – 3t 2 + 2t + 5 r. -5 10. 8v – 5x
  91. 91. Activity 20 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To enhance the students’ skill in dividing polynomials; </li></ul><ul><li>To help the students to be more familiar in dividing polynomials using the long method; and </li></ul><ul><li>To have confidence in dividing polynomials. </li></ul>INSTRUCTION: Perform the indicated operations. 1. (x 11) ÷ (x 4 ) 2. (-4 4x ) ÷ (5 3x )  3. (x 8 ) ÷ (x 3 ) 4. (16m 2 – 25m 2 ) ÷ (4m + 5m) 5. (5x 3 – 14x + 3) ÷ (x-2) 6. (3x 3 – 4x 2 y + 5xy 2 + 6y 3 ) ÷ (x 2 - 2xy +3y 2 ) 7. (9xy 2 – 6x 3 ) ÷ (3x)   Previous Next TABLE OF CONTENTS Answers
  92. 92. 8. (2a 2 b 2 ) ÷ (a 2 b 2 ) 9. (4x 2 y 3 – 24xy 4 ) ÷ (2xy 2 ) 10. (12x 3 y 4 + 18x 4 y 2 – 36xy 3 ) ÷ (3x 2 y 2 ) 11. (7x³y² - 14x⁵y³ + 28x⁸y⁵ - 21x⁵y⁶) ÷ (7x³y²) 12. 4e² ÷ 2e 13. (2y² – 5y – 6) ÷ (2y – 1) 14. (2x²- 5x – 12) ÷ (2x + 3) 15. (3a n + b m ) ÷ (a n b m ) Previous Next Answers
  93. 93. Answers Questions 1 - 7 Questions 8- 15
  94. 94. Activity 21 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To help the students to recall the laws of exponent and signs in dividing polynomials; </li></ul><ul><li>To make the students be familiar in the instructions given; and </li></ul><ul><li>To read the instruction carefully and thoroughly. </li></ul><ul><li>INSTRUCTION: Do what the statement says. Always show your solutions. </li></ul><ul><li>Divide 10m 3 – 2m 2 + 6m – 4 by m 2 – m + 1. </li></ul><ul><li>If we divide the trinomial 14f 2 + 18f – 12 by 12f – 3 what will be the quotient? Box your answer. </li></ul><ul><li>Divide x 2 – 10x + 7 by x + 2. </li></ul><ul><li>What is the second term in the quotient of 2p 4 – p 2 – 5 by p 2 – 1? </li></ul><ul><li>What is the sign of the third term in the quotient of 4n 2 + n – 6n 3 + 3 by 3n 2 + 5? </li></ul><ul><li>Divide 2x 2 – 5x – 6 by 2x – 1. </li></ul><ul><li>Find the quotient of 3a 5 + a 4 b – 3ab 4 – b 5 by 3a + b. Encircle your answer. </li></ul><ul><li>What is the quotient of –u 4 + 2u 3 + u 2 + 4 by u + 2? </li></ul><ul><li>What is the third term in the quotient of y 3 – 1 by y – 1? </li></ul><ul><li>Divide a 7 + a 2 – 2a + 7a 6 + a 5 – 2a 4 + 1 by a – 2. Box your answer and encircle the fifth term of the quotient. </li></ul><ul><li>  </li></ul>Previous Next TABLE OF CONTENTS Answers
  95. 95. Answers Questions
  96. 96. Post Test II Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To enhance the student’s skill in solving the algebraic expression using fundamentals operation. </li></ul><ul><li>To recall all the topics that have discuss by the teacher about solving polynomials using the fundamental operations. </li></ul><ul><li>To have more practice in solving polynomials. </li></ul>Previous Next TABLE OF CONTENTS
  97. 97. <ul><li>INSTRUCTION: Perform the indicated operations and show your solutions. </li></ul><ul><li>Add the following Algebraic Expressions. </li></ul><ul><li>(10a² + 5ab – 3c) + (23a – 15ab + 20c) + (-28a + 16ab – 13c) </li></ul><ul><li>(26x² + 24xy – 18y) + (2x² + 2xy + 2y) </li></ul><ul><li>(41a³ - 75ab² - 38c) + (76a³ + 67ab² + 29c) </li></ul><ul><li>(28a – 2ab – 4b) + (-38b – 46ab – 32a) + (-69b + 22ab + 49a) </li></ul><ul><li>(88x – 44y) + (55x + 22y) </li></ul><ul><li>(37b + 49ab² - 28a³) + ( 34a³ - 32ab² - 25b) </li></ul><ul><li>(59x² + 49y) + (74x² + 54y) </li></ul><ul><li>(13x³ +14y + 24xy²) + (32x³ + 84xy² + 26y) </li></ul><ul><li>(73x + 45xy – 66y) + (64xy – 93y + 82x) </li></ul><ul><li>(18x⁵ - 13xy³ + 12y²) + (12x⁵ - 12xy³ + 12y²) </li></ul>Previous Next Solutions
  98. 98. <ul><li>B. Subtract the following Algebraic Expressions. </li></ul><ul><li>(33x + 12y + 27z) – (46x – 15y + 23z) </li></ul><ul><li>(97x³ +42y² + 52z) – (-51x³ + 48y² - 66z) </li></ul><ul><li>(13x –19y + 14z) – (-13x – 16y + 19z) </li></ul><ul><li>(91x⁶ + 61y⁵) – (31x⁶ - 51y⁵) </li></ul><ul><li>(92a + 72b + 42c) – (82a + 72b + 22c) </li></ul><ul><li>(-35x + 73y – 3z) – (63x – 37y + 23z) </li></ul><ul><li>(-11x³ - 54x² -47x -64) – (-49x³ - 64x² + 49x + 43) </li></ul><ul><li>16xy – 72xy </li></ul><ul><li>(-48x³ + 86y² - 38z) – (-85x³ - 38y² - 82z) </li></ul><ul><li>39ab – 97ab </li></ul>Previous Next Solutions
  99. 99. C. Multiply the following Algebraic Expressions. 11. 6x²(25xy) 12. 42c²(21t) 13. 19x(36xy) 14. 34m²p(86op) 15. 13x(85z) 16. 18j²(17j⁸k⁶) 17. 14h²l⁵(-36t²) 18. 59i⁶l²(61u³v³) 19. 58xyz(34xz) 20. -14f²(62huv) 21. 28xy²(18x²) 22. 92a²b²c(57a³b²c²) 23. 51x(14y)(71z) 24. 76uv(23xyz) 25. 24c(-125n²)(-96c²) Previous Next Solutions
  100. 100. D. Divide the following Algebraic Expressions. 26. (x⁵ ) ÷ (x ² ) 27. (-4 ²x ) ÷ (2 ³x ) 28. (16x 8 ) ÷ (4x 3 ) 29. (10m 2 – 4m 2 ) ÷ (3m + 3m) 30. (10x 3 – 24x + 6) ÷ (x-4) 31. (23x 3 – 44x 2 y + 65xy 2 + 62y 3 ) ÷ (6x 2 - 12xy +24y 2 ) 32. (90xy 2 – 60x 3 ) ÷ (10x) 33. (12a 2 b 2 ) ÷ (6a 2 b 2 ) 34. (14x 2 y 3 – 24xy 4 ) ÷ (5xy 2 ) 35. (12x 3 y 4 + 18x 4 y 2 – 36xy 3 ) ÷ (12x 2 y 2 ) 36. (28x³y² - 14x⁵y³ + 35x⁸y⁵ - 21x⁵y⁶) ÷ (7x³y²) 37. 20e² ÷ 4e 38. (2y² – 5y – 6) ÷ (2y – 1) 39. (22x²- 16x – 12) ÷ (4x + 6) 40. (21a n + b m ) ÷ (7a n b) Previous Next Solutions
  101. 101. Answers Post Test A A. 1. 10a 2 + 5a + 6ab + 4c 2. 28x 2 + 26xy – 16y 3. 117a 3 – 8ab 2 – 9c 4. 45a – 36ab – 111b 5. 143x – 22y 6. 6a 3 + 17ab 2 + 8b 7. 133x 2 + 103y 8. 45x 3 + 108xy 2 + 40y 9. 155x + 109xy – 159y 10. 30x 5 – 25xy 3 + 24y 2
  102. 102. Answers Post Test B B. 1. -13x – 3y + 50z 2. 148x 3 – 6y 2 + 118z 3. 26x – 3y – 5z 4. 60x 6 + 112y 5. 10a + 20c 6. 28x + 110y – 26z 7. 38x 3 + 10x 2 + 96x - 107 8. -56xy 9. 37x 3 + 124y 2 + 44z 10. -58ab
  103. 103. Answers Post Test C 11. 150x 3 y 12.882c 2 t 13. 684x 2 y 14. 2924m 2 op 2 15. 1105xz 16.306j 10 k 2 17. -504h 2 l 5 t 2 18. 5599i 6 l 2 u 3 v 3 19. 1972x 2 yz 2 20. -868f 2 huv 21.504x 3 y 2 22. 5244a 5 b 4 c 3 23. 50694xyz 24. 1748 vxyz 25. 288,oooc 3 n 3
  104. 104. Answers Post Test D
  105. 105. Pre Test III Name:__________________________Score:_____________Date:_____________ Year and Section:__________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To recall all the ways in getting the special products of the polynomial; </li></ul><ul><li>To have more practice solving polynomials; and </li></ul><ul><li>To be more efficient in solving polynomials with their special products. </li></ul>Previous Next TABLE OF CONTENTS
  106. 106. <ul><li>INSTRUCTION: Solve the “SPECIAL PRODUCTS” of the following equations. </li></ul><ul><li>Show your solution and box your final answer. </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><li>(f 2 _ 2c) 2 </li></ul><ul><li>(x + 13) 2 </li></ul><ul><li>(16a 2 + b) 2 </li></ul><ul><li>(2p + 2q) 2 </li></ul><ul><li>(2a m +3z) 2 </li></ul><ul><li>(9y 2 + 5xy) 2 </li></ul><ul><li>(27h x + 6o g ) 2 </li></ul><ul><li>(a – 4) (a + 6) </li></ul><ul><li>(x – 9) (x + 3) </li></ul><ul><li>(m + 8) (m + 5) </li></ul>Previous Next Solutions
  107. 107. 11. (f +2) (f – 8) 12. (w + 4) (w + 11) 13. (s + 5) (s + 6) 14. (c + 10) (c – 3) 15. (a + 8) (a + 9) 16. (i + 25) (i – 3) 17. (i + 25) (i – 3) 18. (m + 5) (m – 6) 19. (h + 3) (h + 5) 20. (l + 6) (l + 9) Previous Next Solutions
  108. 108. <ul><li>21. (ax – 2xy) 3 </li></ul><ul><li>22. (xy 2 + wz 2 ) 3 </li></ul><ul><li>23. (7x 2 + y 4 ) 3 </li></ul><ul><li>(2a + 5b) 2 </li></ul><ul><li>(11a 3 + 4x 2 ) 2 </li></ul><ul><li>(2x + 6) 2 </li></ul><ul><li>(-6xy 2 ) 2 (5x 2 – 6y 4 + 7x) </li></ul><ul><li>ax (9x 2 + ay 2 + a 2 y) </li></ul><ul><li>7ab (cd 2 -9ab –cd 3 ) </li></ul><ul><li>x 3 (3x 2 + 4x – 6 ) </li></ul><ul><li>4xy (12x 2 + 4x + 12y) </li></ul><ul><li>x 3 (5x 2 + 10x + 5) </li></ul><ul><li>(x 4 y 2 ) 2 </li></ul><ul><li>(a 2 c e e m ) 2 </li></ul><ul><li>(21t 3 w 3 ) 2 </li></ul><ul><li>  </li></ul>Previous Next Solutions
  109. 109. Answers 1. f⁴ - 4fc² + 4c² 2. x ² + 26x + 169 3. 256a 4 + 32a 2 + b 2 4. 4p 2 + 8pq + 4q 2 5. 4a 2m + 12a m z + 9q 2 6. 81y 4 + 90xy 3 + 25x 2 y 2 7. 279h 2x + 324h x 0 g + 360 g 8. a 2 + 2a - 24 9. x 2 – 6x - 27 10. m 2 + 13m + 40 11. f 2 – 6f - 16 12. w 2 + 15w + 44 13. s 2 + 11s + 30 14. c 2 + 7c - 30 15. a 2 + 17a + 72 16. i 2 + 21i - 75 17. i 2 + 21i - 75 18. m 2 – m - 30 19. h 2 + 8h + 15 20. l 2 + 15l + 54 21. a 3 x 2 – 6a 2 x 3 y – 12ax 3 y 2 – 8x 3 y 3 22. x 3 y 6 + 3x 2 y 3 wz 2 + 3xy 3 w 2 y 4 + w 3 z 6 23. 1029x 6 + 147x 4 y 4 + 21x 2 y 8 + y 12 24. 4a 2 + 20ab + 25b 2 25. 121a 6 + 88a 3 x 2 + 64x 4 26. 4x 2 + 24x + 36 27. 180x 4 y 4 -216x 2 y 8 + 252x 3 y 4 28. 9ax 3 + a 2 xy 2 + a 3 xy 29. 7abcd 2 – 63a 2 b 2 – 9abcd 3 30. 3x 5 + 4x 4 – 6x 3 31. 48x 3 y + 16x 2 y + 48xy 2 32. 5x 5 + 10x 4 + 5x 3 33. x 8 y 4 34. a 4 c 2e e 2m 35. 441t 6 w 6 Pre Test 21 - 35 Pre Test 11-20 Pre Test 1 - 10
  110. 110. Activity 22 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to square polynomials; </li></ul><ul><li>To enhance the student’s skill in squaring monomials; and </li></ul><ul><li>To have more practice in squaring polynomials. </li></ul><ul><li>INSTRUCTION: Square the following monomials. Encircle your answers. </li></ul><ul><li>(5 x ) 2 </li></ul><ul><li>(4y 3 ) 2 </li></ul><ul><li>(x 4 y 2 ) 2 </li></ul><ul><li>(a 2 c e e m ) 2 </li></ul><ul><li>(k 10 m 3n ) 2 </li></ul><ul><li>(4j n h x+1 ) 2 </li></ul><ul><li>(10m) 2 </li></ul><ul><li>(4xyz 2 ) 2 </li></ul><ul><li>(25m n ) 2 </li></ul><ul><li>(2x 2+n ) 2 </li></ul>Previous Next TABLE OF CONTENTS Answers
  111. 111. Answers 1. 25 2x 2. 16y 6 3. x 8 y 4 4. a 4 c 2e e 2m 5. k 20 m 6n 6. 16j 2n h 2x+2 7. 100m 2 8. 16x 2 y 2 z 2 9. 625m 2n 10. 4 4 + 2n Questions
  112. 112. Activity 23 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To enhance the student’s skill in squaring monomials. </li></ul><ul><li>To make the students be accurate with their answer. </li></ul><ul><li>To have the students some curiosity. </li></ul>INSTRUCTION: Answer the riddle below and show your solution. It is a letter or symbol that is used to represents any elements of a given polynomials.   81x 4 y 2 x 2 y 4 36x 2 y 4 225x 4 y 2 x 2 y 4 81x 2a y 2b 225x 2 y 2 81x 4a y 6b 36x 6 y 2 S = (6x 3 y) 2 A = (xy 2 ) I = (15x 2 y) R = (6XY 2 ) E = (9x 2a y 3b ) B = (9x a y b ) L = (15xy) V = (9x 2 y)   Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ Previous Next TABLE OF CONTENTS Answers
  113. 113. Answers 1. V 2. A 3. R 4. I 5. A 6. B 7. L 8. E 9. S Questions
  114. 114. Activity 24 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To enhance the student’s skill in squaring monomials. </li></ul><ul><li>To be more efficient in squaring monomials. </li></ul><ul><li>To have more practice in squaring monomials </li></ul>INSTRUCTION: Solve the following monomials and box your answer.   1. (7x 3 ) 2 2. (uv 2 ) 2 3. (10x) 2 4. (8y) 2 5. (xy) 2 6. (6m 6x ) 2 7. (13a x b 2y c 5z ) 2 Previous Next TABLE OF CONTENTS Answers
  115. 115. 8. (3a 4 b 3 ) 2 9. (53x 2 ) 2 10. (13x 2 y 2 ) 2 11. (4n x+1 ) 2 12. (5ab 3 ) 2 13. (21t 3 w 3 ) 2 14. (3b a+2 m 2 w 2 ) 2 15. (8l o v e ) 2 Previous Next Answers
  116. 116. Answers 1. 49x 6 2. u 2 v 4 3. 100x 2 4. 64y 2 5.x 2 y 2 6. 36m 12x 7. 169a 2x b 4y c 10z 8. 9a 8 b 6 9. 2809x 4 10. 169x 4 y 4 11. 8n 2x + 2n 12. 25a 2 b 6 13. 441t 6 w 6 14. 9b 2a+4 m 4 w 4 15. 64l 20 v 2e Questions 1 - 7 Questions 8 - 15
  117. 117. Activity 25 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To help the students to avoid guessing the answer. </li></ul><ul><li>To make the students follow the instruction carefully. </li></ul><ul><li>To have more practice in multiplying monomials. </li></ul>INSTRUCTION: Write capital A if the statement is true and small letter a if the statement is false. Show your solution if it is needed.   __________1. In equation 3x 2 (9x 2 + 3x -4), the third of the product is positive 12x 2 .   __________2. ab(a + b +c ) have the product of a 2 b + ab 2 + abc.   __________3. The equation 3bc ( 2a + 3b + 4c + 3d) have the product of trinomial.   __________4. The equation x 2 y 2 (xy + xy 2 + 3xy) is multiplying monomial by trinomial.   __________5. In this equation 4bc(a 2 bc + a 2 b 2 c + 3bc) the product is in the sixth degree.   Previous Next TABLE OF CONTENTS Answers
  118. 118. __________6. The product of the third term of the equation 4c(5a 2 + 2c 2 – 5d + 3b) is -20cd.     __________7. In 2 x + 1 (4 x+1 + y x ), the first term of the product has an exponent of 2x.   __________8. 3(4x + 2y + 3x 2 – y 2 ) have the product of 9x 2 – 3y 2 + 12x +6y.   __________9. In 45x 2 y 2 z 2 (2 x 2 y 2 – 4x 2 y – 3yz 2 ) the third term of the product is 135x 2 y 3 z 4 . Show your solution in the given space and encircle the third term of the product.   ________10. 5j 2 (10ex + 2r 2 – 14i 2 + 13cx) have the product of 50ej 2 x + 10j 2 r 2 + 70i 2 j 2 + 65cx.       Previous Next Answers
  119. 119. Answers 1. a 2. A 3. a 4. A 5. a 6. A 7. a 8. A 9. a 10. a Questions 1 - 5 Questions 6 - 10
  120. 120. Activity 26 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To help the students to enhance their skills in multiplying monomials by polynomials faster; </li></ul><ul><li>To have more practice in multiplying monomials; and </li></ul><ul><li>To show their solution clearly and thoroughly. </li></ul>INSTRUCTION: Perform the indicated operations. Show your solutions and box your answers. 1. x(y 2 + x 2 y + 6) 2. a­­ ­ (4a 2 – 7a – 2) 3. 2x(3x 2 + 4x + 9) 4. 2r(3rst + 30r 2 t + 3s) 5. abc( ab – a + b – 3) 6. ax (9x 2 + ay 2 + a 2 y) 7. 7ab (cd 2 -9ab –cd 3 ) 8. x 3 (3x 2 + 4x – 6 ) 9. 4xy (12x 2 + 4x + 12y) 10. x 3 (5x 2 + 10x + 5) Previous Next TABLE OF CONTENTS Answers
  121. 121. Answers 1. xy 2 + x 3 y + 6x 2. 4a 3 – 7a 2 – 2a 3. 6x 3 + 8x 2 + 18x 4. 6 r2 st + 60r 3 t 5. a 2 b 2 c – a 2 bc + ab 2 c – 3abc 6. 9ax 3 + a 2 xy 2 + a 3 xy 7. 7abcd 2 – 63a 2 b 2 – 7abcd 3 8. 3x 5 + 12x 4 – 6x 3 9. 48x 3 y + 16x 2 y + 48xy 2 10. 5x 5 + 10x 4 + 5x 3 Questions
  122. 122. Activity 27 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To make the students practice in more equation. </li></ul><ul><li>To be more accurate with their answer. </li></ul><ul><li>To have more patient in solving an equation. </li></ul>INSTRUCTION: Perform the following equation in the indicated operation and show your solution. Make your answer inside the box. 1. 14x 2 (4xy 2 + 27x +x 4‑­­ ) 5. -7h(4g 2 + 7y – 6r)   2. 2y(y 2 + 4y – 21 ) 6. 8 x (5t 2 + 3x 3 – 5)   3. 21dp (3d 2 + 9d) 7. (-6xy 2 ) 2 (5x 2 – 6y 4 + 7x)   4. 15p 2 q(48pq – x 2 ) 8. 11e 3 j 2 (6e 2x + 2j 2r – 6)   Previous Next TABLE OF CONTENTS Answers
  123. 123. Answers 1. 56x 3 y 2 + 378x 3 + 14x 6 2. 2y 3 + 8y 2 - 42 3. 63d 3 p + 189d 2 p 4. 720p 3 q 2 – 15 p 2 qx 2 5. -28q 2 h – 49hy + 42hr 6. 40t 2x + 24x 3x – 40 x 7. 180x 4 y 4 – 216x 2 y 8 + 252x 3 y 4 8. 66e 6x j 2 + 22e 3 j 4t – 66e 3 j 2 Questions
  124. 124. Activity 28 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to square a binomial; </li></ul><ul><li>To help the students to square a binomial; and </li></ul><ul><li>To enhance the skills of the students in squaring binomial. </li></ul><ul><li>INSTRUCTION: Square the following binomials and show your complete solutions. Box your answers. </li></ul><ul><li>(4a +b) 2 </li></ul><ul><li>(2x + 3y) 2 </li></ul><ul><li>(4u + 3v) 2 </li></ul><ul><li>(8a + 3u) 2 </li></ul><ul><li>(5a – b) 2 </li></ul><ul><li>(2a + 5b) 2 </li></ul><ul><li>(5t 2 + 5d) 2 </li></ul><ul><li>(12e 3 – j 4 ) 2 </li></ul><ul><li>4y 2 + 4z 3 ) 2 </li></ul><ul><li>(11a 3 + 4x 2 ) 2 </li></ul><ul><li>  </li></ul><ul><li>  </li></ul>Previous Next TABLE OF CONTENTS Answers
  125. 125. Answers 1. 16a 2 + 8ab + b 2 2. 4x 2 + 12xy + 9y 2 3. 16u 2 + 24uv + 9v 2 4. 64a 2 + 48au + 9u 2 5. 25a 2 – 10 ab + b 2 6. 4a 2 + 20 ab + 25b 2 7. 25t 4 + 50dt 2 + 25d 2 8. 144e 6 – 24e 3 j 4 +j 8 9. 16y 4 + 32y 2 z 3 + 16z 6 10. 121a 6 + 88a 3 + 16x 4 Questions
  126. 126. Activity 29 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To help the students to enhance their skills in squaring binomial. </li></ul><ul><li>To show their solution accurately. </li></ul><ul><li>To have confidence in squaring binomial. </li></ul><ul><li>INSTRUCTION: Square the following binomials. Show your solution and encircle your answer. </li></ul><ul><li>  </li></ul><ul><li>(y – 9) 2 </li></ul><ul><li>(2x + 6) 2 </li></ul><ul><li>(x 2 + 1) 2 </li></ul><ul><li>(y 2 _ 4y) 2 </li></ul><ul><li>(x + 3) 2 </li></ul><ul><li>(3b 2 + b) 2 </li></ul><ul><li>(2x + 1) 2 </li></ul><ul><li>  </li></ul><ul><li>  </li></ul>Previous Next TABLE OF CONTENTS Answers
  127. 127. <ul><li>(2x -3y) 2 </li></ul><ul><li>(2x 2 + 6x) 2 </li></ul><ul><li>(27x 2 + y) 2 </li></ul><ul><li>(y 2 – 13y) 2 </li></ul><ul><li>(x 2 + 4) 2 </li></ul><ul><li>(2x – 10) 2 </li></ul><ul><li>(2x + 8) 2 </li></ul><ul><li>(x 3 – 4x) 2 </li></ul>Previous Next Answers
  128. 128. Answers 1. y 3 – 18y +81 2. 4x 3 + 24x +36 3. x 4 + 2x 2 + 1 4. y 4 – 8y 3 + 16y 2 5. x 2 + 6x + 9 6. 9b 4 + 6b 3 + b 2 7. 4x 2 4x + 1 8. 4x 2 – 12xy + 9y 2 9. 4x 4 + 24x 3 + 36x 10. 729x 4 + 54x 2 y + y 4 11. y 4 – 26y 3 – 169y 2 12. x 4 + 8x 2 + 16x 13. 4x 2 – 40x + 100 14. 4x 2 + 32x + 64 15. x 6 – 84 4 + 16x 2 Questions 1 – 7 Questions 8 - 15
  129. 129. Activity 30 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ Objectives: 1. To help the students to enhance their skills in squaring binomial. 2. To have the student a mastery in squaring binomial. 3. To have more patient in squaring a binomial. INSTRUCTION: Solve the following binomial and show your complete solution. Encircle your answer.   1. (5y – 1) 2 6. (5a 3 + x 2 ) 2 2. (2c + d) 2 7. (y – 2) 2 3. (x 2 + 2y) 2 8. (2xy – 4x) 2 4. (5at – 1) 2 9. (8x – 2 ) 2 5. (3x 2 + 2x 2 ) 2 10. (3x 2 + 2y) 2 Previous Next TABLE OF CONTENTS Answers
  130. 130. Answers 1. 25y 2 – 10y + 1 2. 4c 2 + 4cd + d 2 3. x 4 + 4x 2 y + 4y 2 4. 25a 2 t 2 – 10at + 1 5. 9x 4 +12x 4 + 4x 4 or 25x 4 6. 25a 6 + 10a 3 x 2 + x 4 7. y 2 – 4y + 4 8. 4x 2 y 2 – 16x 3 y – 16x 3 9. 64x 2 – 32x + 4 10. 9x 4 + 12x 2 y + 4y 2 Questions
  131. 131. Activity 31 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To help the students to enhance their skills in cubing binomial. </li></ul><ul><li>To have the student a mastery in cubing binomial. </li></ul><ul><li>To have some confidence in cubing binomial. </li></ul><ul><li>INSTRUCTION: Solve the following binomial. Show your complete solution and box your answer. </li></ul><ul><li>(x + y) 3 </li></ul><ul><li>(2x + 4y) 3 </li></ul><ul><li>(3x 3 + 5y) 3 </li></ul><ul><li>(x – y) 3 </li></ul><ul><li>(4a – 2y) 3 </li></ul><ul><li>(7m + 3n) 3 </li></ul><ul><li>(8b + 4y) 3 </li></ul>Previous Next TABLE OF CONTENTS Answers
  132. 132. 8. (12c 2 – 6x 2 ) 3 9. (3b 3 – 7y) 3 10. (6e 2 + 3j) 3 11. (9a 3 – 7m) 3 12. (4d 2 + 3f) 3 13. (3q 2 – 4k) 3 14. (6k 2 – 5y) 3 15. (8x – 12y) 3   Previous Next Answers
  133. 133. Answers 1. x 3 + 3x 2 y + 3xy 2 + y 3 2. 8x 3 + 48x 2 y + 96xy 2 + 64y 3 3. 27x 9 + 135x 6 y + 225x 3 y 2 + 125y 3 4. x 3 - 3x 2 y + 3xy 2 – y 3 5. 64a 3 – 96a 2 y + 48ay 2 – 8y 3 6. 343m 3 + 441m 2 n + 189mn 2 + 27n 3 7. 512b 2 + 768b 2 y + 384by 2 + 64y 3 8. 1728c 6 – 2592c 4 x 2 + 1296c 2 x 4 – 216x 6 9. 27b 9 – 189b 6 y + 441b 3 y 2 – 343y 3 10. 216e 6 + 324e 4 j + 162e 2 j 2 + 27j 3 11. 729a 9 – 1701a 6 m + 1323a 3 m 2 – 343m 3 12. 64d 6 + 144d 4 f + 108d 2 f 2 + 27f 3 13. 27q 6 – 108q 4 k + 144k 2 q – 64k 3 14. 216k 6 – 540k 4 y + 450k 2 y 2 - 125y 3 15. 512x 3 – 2304x 2 y + 3456xy 2 – 1728y 3 Questions 1 - 7 Questions 8 - 15
  134. 134. Activity 32 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to cube binomials. </li></ul><ul><li>To show complete solution clearly. </li></ul><ul><li>To have a confidence in cubing binomials. </li></ul><ul><li>INSTRUCTION: Solve the following binomial. Show your complete solution. Box your answer. </li></ul><ul><li>(2x – 3y) 3 </li></ul><ul><li>(x – 2) 3 </li></ul><ul><li>(2x + 2a) 3 </li></ul><ul><li>(5x – 3y) 3 </li></ul><ul><li>(2a + b) 3 </li></ul><ul><li>(2y – z) 3 </li></ul><ul><li>(x – 5) 3 </li></ul><ul><li>(2x + 7y) 3 </li></ul><ul><li>(2ay 2 – 4ay) 3 </li></ul><ul><li>(c 2 – d 2 ) 3 </li></ul>Previous Next TABLE OF CONTENTS Answers
  135. 135. Answers 1. 8x 2 – 36x 2 y + 54xy 2 – 27y 3 2. x 2 – 6x 2 + 12x - 8 3. 8x 3 + 24ax 2 + 24a 2 x + 8a 3 4. 125x 3 – 225x 2 y + 135xy 2 – 27y 3 5. 8a 3 + 12a 2 b + 6ab 2 – b 3 6. 8y 3 + 12y 2 z + 6yz 2 – z 3 7. x 3 – 15x 2 + 75x - 125 8. 8x 3 + 84x 2 y + 294xy 2 + 343y 3 9. 8a 3 y 6 – 48a 3 y 5 – 96a 3 y 4 – 64a 3 y 3 10. c 6 – 3c 4 d 2 + 3c 2 d 4 – d 6 Questions
  136. 136. Activity 33 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To have the student a mastery in cubing binomial. </li></ul><ul><li>To know the relationship of squaring a binomials and cubing a binomials. </li></ul><ul><li>To be have more patient in squaring and cubing binomials. </li></ul><ul><li>INSTRUCTION: Cube the following binomials. Show your complete solution in the box. </li></ul><ul><li>(3x + 4y) 3 </li></ul><ul><li>(7x 2 + y 4 ) 3 </li></ul><ul><li>(4f -8y) 3 </li></ul><ul><li>(4y 3 + 3y 2 ) 3 </li></ul><ul><li>(xy 2 + wz 2 ) 3 </li></ul><ul><li>(3w + 4z) 3 </li></ul><ul><li>(y 3 - 8) 3 </li></ul><ul><li>(9l + 8t) 3 </li></ul><ul><li>(2o 3 + 2x 4 ) 3 </li></ul><ul><li>(ax – 2xy) 3 </li></ul>Previous Next TABLE OF CONTENTS Answers
  137. 137. Answers 1. 27x 3 + 108x 2 y + 144xy 2 + 64y 3 2. 343x 6 + 147x 4 y 4 – 21x 2 y 8 + y 2 3. 64f 3 – 384f 2 y + 768fy 2 – 512y 3 4. 64y 9 + 144y 8 + 108y 7 + 27y 6 5. x 3 y 6 + 3x 2 y 4 wz 2 + 3xy 2 w 2 z 4 + w 3 z 6 6. 27w 3 + 108w 2 z + 144wz 2 + 64z 3 7. y 9 – 24y 6 + 192y 3 - 512 8. 729l 3 + 1944l 2 t + 1728lt 2 + 512t 3 9. 8o 9 + 24o 6 x 4 + 24o 3 x 8 + 8x 12 10. a 3 x 3 – 6a 2 x 3 y + 12ax 3 y 2 – 8x 3 y Questions
  138. 138. Activity 34 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to solve the special products of binomial. </li></ul><ul><li>To have more practice in solving the special products of binomial. </li></ul><ul><li>To have more patient in solving an equation. </li></ul><ul><li>INSTRUCTION: Solve the following binomial and get their special products. Show your complete </li></ul><ul><li>solution and box your answer. </li></ul><ul><li>  </li></ul><ul><li>(a + 2)(a + 8) </li></ul><ul><li>(l + 6) (l + 9) </li></ul><ul><li>(e + 5) (e + 7) </li></ul><ul><li>(t + 2) (t + 6) </li></ul><ul><li>(h + 3) (h + 5) </li></ul><ul><li>(x + 4) (x + 2) </li></ul><ul><li>(m + 5) (m – 6) </li></ul><ul><li>  </li></ul>Previous Next TABLE OF CONTENTS Answers
  139. 139. 8. (j 2 + 6) (j 2 + 8) 9. (e 3 + 2) (e 3 – 4) 10. (r 4 – 3) (r 4 + 5) 11. (3x + 8)(7x + 9) 12. (2x + 4)(4x + 6) 13. (5x + 2)(3x + 4) 14. (6x + 3)(4x + 2) 15. (2x + 4)(8x + 5) Previous Next Answers
  140. 140. Answers 1. a 2 + 109 + 16 2. l 2 + 15l + 54 3. e 2 + 12e + 35 4. t 2 + 8t + 12 5. h 2 + 8h + 15 6. x 2 + 6x + 8 7. m 2 – m – 30 8. j 4 + 14j 2 + 48 9. e 6 – 2e 3 – 8 10. r 8 + 2r – 15 11. 21x 2 + 83x + 72 12. 8x 2 + 28x + 24 13. 15x 2 + 26x + 8 14. 24x 2 + 24x + 6 15. 16x 2 + 42x + 20 Questions 1 - 7 Questions 8 - 15
  141. 141. Activity 35 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To have a mastery in getting the special products of the binomials. </li></ul><ul><li>To be more efficient in using the FOIL method. </li></ul><ul><li>To have more patient in solving an equation. </li></ul><ul><li>INSTRUCTION: Encircle the product of the following equation and box the third term of each product. </li></ul><ul><li>  </li></ul><ul><li>(x - 20) (x + 3) </li></ul><ul><li>(y + 1) (y – 2) </li></ul><ul><li>(k + 30) (k + 5) </li></ul><ul><li>(a – 4) (a + 6) </li></ul><ul><li>(x – 9) (x + 3) </li></ul><ul><li>(m + 8) (m + 5) </li></ul><ul><li>(f +2) (f – 8) </li></ul>Previous Next TABLE OF CONTENTS Answers
  142. 142. 8. (w + 4) (w + 11) 9. (j + 5) (j – 3) 10. (x + 19) (x – 6) 11. (3x + 5) (2x + 35) 12. (3x 2 + 3) (3x 2 + 25) 13. (4a + 14) (6a + 39) 14. (5r + 7) (8r + 3) 15. (9q 2 + 2)(2q 2 – 5) Previous Next Answers
  143. 143. Answers 1. x 2 – 17x - 60 2. y 2 – y – 2 3. k 2 + 35 k + 150 4. a 2 + 2a – 24 5. x 2 – 6x – 27 6. m 2 + 13m + 40 7. f 2 – 6f - 16 8. w 2 + 15w + 44 9. j 2 + 2y – 15 10. x 2 + 13x - 114 11. 6x 2 + 115x + 175 12. 9x 4 + 84x 2 + 75 13. 24a 2 + 240a + 546 14. 40r 2 + 71r + 21 15. 18q 4 – 41q 2 - 10 Questions 1 – 7 Questions 8 - 15
  144. 144. Activity 36 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To have more practice in solving the special products of binomial. </li></ul><ul><li>To have more practice in solving the special products of binomial. </li></ul><ul><li>To have more patient in solving an equation. </li></ul><ul><li>INSTRUCTION: Solve the equation in the circle and box the product. </li></ul><ul><li>(i + 25) (i – 3) </li></ul><ul><li>(i + 25) (i – 3) </li></ul><ul><li>(o + 13) (o – 2) </li></ul><ul><li>(x+ 5) (x – 1) </li></ul><ul><li>(a + 8) (a + 9) </li></ul><ul><li>(a + 9) (a – 11) </li></ul><ul><li>(p + 5) (p + 4) </li></ul><ul><li>(s + 5) (s + 6) </li></ul><ul><li>(c + 10) (c – 3) </li></ul><ul><li>(q 2 + 5) (q 2 – 2) </li></ul>Previous Next TABLE OF CONTENTS Answers
  145. 145. Answers 1. i 2 + 22i - 75 2. i 2 + 22i - 75 3. 0 2 + 11o - 26 4. x 2 + 4x - 5 5. a 2 + 17a + 72 6. a 2 – 2a – 99 7. p 2 + 9p + 20 8. s 2 + 11s + 30 9. c 2 + 7c - 30 10. q 4 + 3q 2 - 10 Questions
  146. 146. Post Test III Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ <ul><li>Objectives: </li></ul><ul><li>To recall all the ways in getting the special products of the polynomial. </li></ul><ul><li>To have more practice solving polynomials. </li></ul><ul><li>To be more efficient in solving polynomials with their special products. </li></ul>Previous Next TABLE OF CONTENTS A B C
  147. 147. <ul><li>INSTRUCTION: Solve the following polynomials and get their special products. </li></ul><ul><li>Show your solution and box your final answer. </li></ul><ul><li>  </li></ul><ul><li>A. Square the following monomials and binomials. </li></ul><ul><li>(er 3 ) 2 </li></ul><ul><li>(5y 2 ) 2 </li></ul><ul><li>(12d) 2 </li></ul><ul><li>(7jy) 2 </li></ul><ul><li>(vx) 2 </li></ul><ul><li>(7k 4x ) 2 </li></ul><ul><li>(2w a y 2h z 3z ) 2 </li></ul><ul><li>(12r 5 t 6 ) 2 </li></ul><ul><li>(26m 3a ) 2 </li></ul><ul><li>(13kl 2 t 6 ) 2 </li></ul><ul><li>(u – 10) 2 </li></ul><ul><li>(2x 7y + 3) 2 </li></ul><ul><li>(5x a +2) 2 </li></ul><ul><li>(f 2 _ 2c) 2 </li></ul><ul><li>(x + 13) 2 </li></ul><ul><li>(16a 2 + b) 2 </li></ul><ul><li>(2p + 2q) 2 </li></ul><ul><li>(2a m +3z) 2 </li></ul><ul><li>(9y 2 + 5xy) 2 </li></ul><ul><li>(27h x + 6o g ) 2 </li></ul><ul><li>  </li></ul>Previous Next Solutions
  148. 148. <ul><li>B. Cube the following binomials </li></ul><ul><li>(5ax – 23by) 3 </li></ul><ul><li>(2x – 6) 3 </li></ul><ul><li>(2fx + 2h) 3 </li></ul><ul><li>(5c – 4) 3 </li></ul><ul><li>(7a +2k) 3 </li></ul><ul><li>(8y k – z) 3 </li></ul><ul><li>(2x 2 – 3) 3 </li></ul><ul><li>(5k + 8l) 3 </li></ul><ul><li>(7ax 2 – 2ay) 3 </li></ul><ul><li>(3hx +7y) 3 </li></ul>Previous Next Solutions
  149. 149. <ul><li>C. Solve the following equations. </li></ul><ul><li>a 2 (f 2 + a 2 y + 6) </li></ul><ul><li>m(6a 2 – 9a – 10) </li></ul><ul><li>4x(2x 3 + gx + 8) </li></ul><ul><li>3r(2rst + 20r 2 t + 3s) </li></ul><ul><li>mno(mn – m + o – 3) </li></ul><ul><li>kx (9k 2 + kxy 2 + k 2 y) </li></ul><ul><li>2ab (3cd 2 -7ab –5cd 3 ) </li></ul><ul><li>x 6 (2x+ 3x – 5 ) </li></ul><ul><li>2xz (14x 3 + 4y + 12z) </li></ul><ul><li>x 5 (8x 2 + 23x + 7) </li></ul><ul><li>12x 2 (5xy 2 + 17x +x 3 ) </li></ul><ul><li>(s + 3) (s – 7) </li></ul><ul><li>(m + 16) (m – 32) </li></ul><ul><li>(x + 2) (x – 5) </li></ul><ul><li>(t + 11) (t + 19) </li></ul><ul><li>  </li></ul>Previous Next Solutions
  150. 150. <ul><li>(k + 5) (k – 18) </li></ul><ul><li>(q + 2) (q + 4) </li></ul><ul><li>(y + 3) (y + 7) </li></ul><ul><li>(u + 15) (u – 2) </li></ul><ul><li>(x 2 + 2) (x 2 – 4) </li></ul><ul><li>(w 3 + 5) (w 3 + 8) </li></ul><ul><li>(3l + 7) (4l + 2) </li></ul><ul><li>(2x 2 + 4) (3x 2 + 6) </li></ul><ul><li>(2y + 15) (6y + 33) </li></ul><ul><li>(5t + 3) (4t + 8) </li></ul><ul><li>(3q 2 + 1)(2q 2 – 9) </li></ul><ul><li>(11v + 2) (5v + 1) </li></ul><ul><li>(2u a + 1) (8u a + 2) </li></ul><ul><li>(7b – 2)(3b – 6) </li></ul><ul><li>(24x – 1) (27x + 2) </li></ul><ul><li>  </li></ul>Previous Next Solutions
  151. 151. Answers 1. e 2 r 6 2. 25y 4 3. 144d 2 4. 49j 2 y 2 5. y 2 x 2 6. 49k 8x 7. 4w 29 y 4h z 6z 8. 144r 10 t 12 9. 676m 6a 10. 169k 2 l 4 t 12 11. u 2 – 20u + 100 12. 4x 14y + 12x 7y +9 13. 25x 2a + 20xa + 4 14. f 4 - 4cf 2 + 4c 2 15. x 2 + 26x + 169 16. 256a 2 + 32a 2 b + b 2 17. 4p 2 + 8pq + 4q 2 18. 4a 2m + 12a m z + 9z 2 19. 81y 4 + 90xy 3 + 25x 2 y 2 20. 729h 2x + 324h x o g + 36o 2g Questions A
  152. 152. Answers 1. 12a 3 x 2 – 175a 2 bx 2 y + 7 935ab 2 xy 2 – 12 167b 3 y3 2. 8x 3 – 72x 2 + 216x - 216 3. 8f 3 x 3 + 24f 2 hx 2 + 24fh 2 x + 8h 3 4. 125c 3 – 300c 2 + 240c - 64 5. 343a 3 + 294a 2 k + 84ak 2 + 8k 3 6. 512y 3k – 192y 2k z – 24y k z 2 – z 3 7. 8x 6 – 36x 4 – 54x 2 - 27 8. 125k 3 – 600k 2 l + 960kl 2 + 512l 3 9. 343a 3 x 6 – 294a 3 x 4 y + 84a 3 x 2 y 2 – 8a 3 y 3 10. 27h 3 x 3 – 189h 2 x 2 y + 441hxy 2 + 343y 3 Questions B
  153. 153. Answers 1. a 2 f 2 – a 4 y + 6a 2 2. 6a 2 m – 9am – 10m 3. 8x 4 + 4ax 2 + 32x 4. 6r 2 st + 60r 3 t + 9rs 5. m 2 n 2 o – m 2 no + mno 2 – 3mno 6. 9k 3 x + k 2 x 2 y 2 + k 3 xy 7. 6abcd 2 – 14a 2 b 2 – 10abcd 3 8. 5x 7 – 5x 6 9. 28x 4 z + 8xyz + 24xz 2 10. 8z 7 + 25x 6 + 7x 5 11. 60x 3 y 2 + 204x 3 + 12x 5 12. s 2 – 4s - 21 13. m 2 – 16m + 512 14. x 2 – 3x - 10 15. t 2 + 30t + 209 Questions C_1 - 15
  154. 154. Answers 16. k 2 – 13k - 90 17. q 2 + 6q + 8 18. y 2 + 10y + 21 19. u 2 + 13u - 30 20. x 4 – 2x 2 – 8 21. w 6 + 13w 3 + 40 22. 12l 2 + 34l + 14 23. 6x 4 + 24x 2 + 24 24. 12y 2 + 146y + 495 25. 20t 2 + 52t + 24 26. 6q 4 – 16q - 9 27. 55v 2 + 21v + 2 28. 16u 2a + 12u a + 2 29. 21b 2 – 48b + 12 30. 648x 2 + 21x - 2 Questions C_1 - 15
  155. 155. Pre Test IV Name: __________________________ Score:_____________Date:_______________ Year and Section: ________________ Teacher: _______________________________ <ul><li>Objectives: </li></ul><ul><li>To recall different types of factoring polynomial. </li></ul><ul><li>To get and write the factors of the polynomials. </li></ul><ul><li>To have patience in finding the factor of a polynomial. </li></ul><ul><li>To increase proficiency in factoring a polynomials. </li></ul>TABLE OF CONTENTS TABLE OF CONTENTS PREVIOUS NEXT A , B C , D E , F G , H I , J K , L M , N O
  156. 156. A. Instruction: Tell whether if the common factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor __________1. The factor of 2x² - 6x + 8 is 2(x²– 3x + 4). __________2. The factor of 5x + 30 is 5(x + 6). __________3. The factor of 24x³ - 64y³ is 8(3x³ + 8y³). __________4. The factor of 625x³ - 100y² is 25(25x³ + 5y²). __________5. The factor of 2x³ + 4x² - 10x is 2(x³ + 2x² - 5x). B. Instruction: Match the polynomial in column A to its proper and common factor in column B . Write the letter of your answer in the space provided before each number. A B _____1. 3x + 9y a. 5 (x + 6) _____2. 2x³ + 4x² - 10x b. 2x (x² - 2x – 3) _____3. 6a³b + 3a²b² - 18ab³ c. 2x (x² + 2x – 5) _____4. 5x + 30 d. 3 (x + 3y) _____5. 2x³ - 4x² - 6x e. 3 (3a³b + a²b² - 6ab³) PREVIOUS NEXT ANSWERS
  157. 157. C. Instruction: Factor the following algebraic expression. Get their common factor. Write your answer in the space provided. 1. 6c 4 – 8c³ - 2c² 2. 2b³ - 4b² - 8b + 10 3. 3y⁶ - 12y³ - 5y 4. 3ax² - 6a²x + 9a³x 5. 18x² - 24xy + 3y² D. Instruction: Tell whether if the factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor.   _____1. The factor of m² - 144 is (m + 7) (m + 7). _____2. The factor of b²x² - y² is (b + y) (x – y). _____3. The factor of 25 - p² is (5 + p) (5 – p). _____4. The factor of 64x²y² - x² is (8xy + y) (8xy – x). _____5. The factor of c² - d⁴ is (c + d²) (c - d²).   PREVIOUS NEXT ANSWERS
  158. 158. E. Instruction: Tell whether if the factor by grouping of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor.   _____1. The factor of ax + ay + bx + by is (a + b) (x + y). _____2. The factor of 2x +8y – 3px -12py is (2 – 3p) (x + 4y). _____3. The factor of 3x – 3y + 4ay – 4ax is (3 – 4a) (x – y). _____4. The factor of x³ + 7x² + 2x ² 14 is (x² + 2) ( x + 7). _____5. The factor of 3x² + xy -12x -4y is (x – 4) (3x + y). F. Instruction: Match the polynomials in column A to its proper factor of grouping in column B . Write your answer in the space provided before each number.   A B _____1. 15x⁴ - 15x² + 5x² a. 2a³b² (a² + 4ab - 2b²) _____2. 2a⁵b² + 8a⁴b³ -4a³b⁴ b. (4x – 5) (x + 3) _____3. a³ -2a² + 5a – 10 c. 5x² (x² - 3x + 1) _____4. 3xy + 21x -2y – 14 d. (a – 2) (a² + 5) _____5. 5x² + 11x + 2 e. (x – 4y) (2x + 3y) PREVIOUS NEXT ANSWERS
  159. 159. G. Instruction: Factor the following algebraic expressions by grouping. Write your answer in the space provided. 1. 27x³ + 108x² + 144x + 64 2. 4b² + 12bc + 9c² - 25d 3. 36x² - 9y² + 24yz- 16z² 4. ax² -4a + 3x² - 12 36x² - 9y² + 24yz – 16z²   H. Instruction: Match polynomials in column A to its correct factoring which is the difference of two squares in column B . Write your answer in the space provided before each number.   A B _____1. x² - 9 a. (x⁴ + y⁴) (x² + y²) (x + y) (x – y) _____2. 4x² - 36y⁶ b. 4xy (2x + 3y) (2x - 3y) _____3. 49x⁴ - 36y⁴ c. (x + 3) (x – 3) _____4. x⁸ - y⁸ d. (7x² + 6y²) (7x² - 6y²) _____5. (t + 4)² - 9 e. (t + 7) (t + 1)   PREVIOUS NEXT ANSWERS
  160. 160. <ul><li>Instruction: Factor the difference of the two squares of the given polynomials. </li></ul><ul><li>Write your answer in the space provided. </li></ul><ul><li>  </li></ul><ul><li>1. 81a² - 256b⁴ </li></ul><ul><li>2. 100 – 169z² </li></ul><ul><li>3. 121 – 100x²y² </li></ul><ul><li>4. 25m² - 36n² </li></ul><ul><li>5. 64x²y⁴ - 1 </li></ul>J. Instruction: Find the missing term to make the expression a perfect trinomial square.   1. x + __________ + 9 2. a² + 8a + _______ 3. ______ + 2ab + b² 4. 64x²y² + 80xyz + ________ 5. 25a² + _______ + 16b² PREVIOUS NEXT ANSWERS
  161. 161. K. Instruction: Match polynomials in column A to its correct factor which is a perfect trinomial square in column B .   A B _____1. 4x² + 4x + 1 a. (2x + 3)² _____2. 25y² - 40y + 16 b. (2x + 1)² _____3. x² - 8x + 16 c. (x – 4)² _____4. a² + 14a + 49 d. (a + 7)² _____5. 4x² + 12x + 9 e. (5y – 4)² L. Instruction: Factor the following polynomials by a perfect trinomial square. Write you answer in the space provided.   1. x² + 12x + 36 2. x² + 12xy + 9y² 3. x² - 4x + 4 4. x² + 8x + 16 5. 36a² - 48a + 16 PREVIOUS NEXT ANSWERS
  162. 162. M. Instruction: Tell whether if the factor of the following equations is a factor of general quadratic trinomial. Write A if the factor is correct and B if the factor is incorrect and write the correct factor.   _____1. The factor of 8p² + 24p + 18 is (2p + 3) (4p + 6). _____2. The factor of 15x² + 41x + 28 is (3 + 4) (5x + 7). _____3. The factor of 12b² + 17b – 5 is (2b + 1) ( 6b – 5) _____4. The factor of 24m² + 50mn – 9 is (4m + 3) (6m – 3). _____5. The factor of 6y² + 7y - 20 is (3y + 10) (2y – 2). N. Instruction: Match the polynomials in column A to its correct factor which is in the general equation in column B .   A B _____1. (4x – 5) (x + 3) a. 3x² + 17x + 20 _____2. (x + 5) (x + 5) b. x² + 10x + 25 _____3. (p – 3) (p + 2) c. 2x² - 10 x + 12 _____4. (2x – 6) (x – 2) d. p² - p – 6 _____5. (x + 4) (3x + 5) e. 2x² - 10x + 12 PREVIOUS NEXT ANSWERS
  163. 163. O. Instruction: Factoring the sum and difference of cubes of the following polynomials. Write the letter of your answer in the space provided.   1. x³ - 8 2. 27x³ + 1 3. x³y⁶ - 64 4. 8x³ + 27 5. x³ + 1   PREVIOUS NEXT ANSWERS
  164. 164. A. 1. A 2. A 3. A 4. B 25(25x³ - 5y²) 5. A Answers B. 1. D 2. C 3. E 4. A 5. B C. 1. 2c 2 (3c 2 – 4c - )1 2. 2(b 3 – 2b 2 – 4b + 5 3. y(3y 5 – 12y 2 – 5) 4. 3ax(x – 2a + 3a 2 ) 5. 3(6x 2 – 8xy + y 2 ) D. 1.B (m + 12) (m – 12) 2. B (bx – y) (bx + y) 3. A 4. B (8xy – x) (8xy +x 5. A Questions A Questions C Questions B Questions D E. 1. A 2. A 3. B (3 + 4a) ( x – y) 4. A 5. A F. 1. C 2. A 3. D 4. E 5. B G. 1. 2. 3. 4. 5. H. 1. C 2. B 3. D 4. A 5. E Questions H Questions G Questions F Questions E
  165. 165. I. 1. (9a+16b 2 )(9a-16b 2 2.(5+13z)(5 -13z) 3. (11-10xy)(11+10xy) 4. (5m–6n)(5m+6n) 5. (8xy 2 –1) (8xy 2 +1) O. 1. (x-2) (x² - 2x + 4) 2. (3x + 1) (9x² +3x + 1) 3. (xy - 8) (x 2 y 5 -8xy+ 8) 4. (2x + 3) (4x 3 +6x + 9) 5. (x + 1) (x 2 + x + 1) N. 1. E 2. B 3. D 4. C 5. A J. 1. 6x 2. 16 3. a 2 4. 25 5. 40ab M. 1. A 2. A 3. B (4b - 1) ( 3b + 5) 4. B (6m - 1) (4m + 9) 5. B (3y - 4) (2y + 5). K. 1. B 2. E 3. C 4. D 5. A L. 1. (x+6) 2 2.(x+3) 2 3. (x – 2) 2 4. (x+4) 2 5. (6a – 4) 2 Questions I Questions J Questions K Questions L Questions O Questions M Questions N
  166. 166. Activity 37 Name: _________________________Score:_________Date:___________ Year and Section: ________________ Teacher: ______________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to factor a polynomial out of common factor. </li></ul><ul><li>To get and write the common factor. </li></ul><ul><li>To increased proficiency in factoring a polynomial out of common factor. </li></ul>Instruction: Tell whether if the common factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of 2x² - 6x + 8 is 2(x²– 3x + 4). _____2. The factor of 5x + 30 is 5(x + 6). _____3. The factor of 24x³ - 64y³ is 8(3x³ + 8y³). _____4. The factor of 625x³ - 100y² is 25(25x³ + 5y²). _____5. The factor of 2x³ + 4x² - 10x is 2(x³ + 2x² - 5x). _____6. The factor of 16x² - 24xy is 8(2x – 3y). _____7. The factor of 6a² - 9ab is 3(2a² - 3b). _____8. The factor of 12a²b – 18a³b is 6a(2b – 3ab). _____9. The factor of 9ay + 3a² - 6ay² is 3a(3ay + a² - 2ay²). _____10. The factor of 2n² - 6n + 4 is 2(n² - 3 + 2).   Previous Next TABLE OF CONTENTS Answers
  167. 167. Answers 1. A 2. A 3. B 8(3x 3 – 8y 3 ) 4. B 25(25x 3 – 4y 2 ) 5. A 6. B 8x(2x – 3y) 7.B 3a(2a – 3b) 8. B 6ab(2a – 3a 2 ) 9. B 3a(3y + a – 2y 2 ) 10. B 2(n 2 – 3n + 2) Questions
  168. 168. Activity 38 Name:_______________________Score:_____________Date:_____________ Year and Section: _________________Teacher: _________________________ <ul><li>Objectives: </li></ul><ul><li>To identify the common factor of a polynomial. </li></ul><ul><li>To get and write the common factor. </li></ul><ul><li>To increase proficiency in factoring a polynomial out of common factor. </li></ul>Instruction: Match the polynomial in column A to its proper and common factor in column B . Write the letter of your answer in the space provided before each number. A B _____1. 3x + 9y a. 2(x² - 3x + 4) _____2. 2x³ + 4x² - 10x b. 25(25x³ - 5y²) _____3. 6a³b + 3a²b² - 18ab³ c. 2x(x² - 2x – 3) _____4. 5x + 30 d. 5(x + 6) _____5. 2x³ - 4x² - 6x e. 8 (3x² - 8y²) _____6. 625x³ - 100y² f. 2x(x² - 2x – 3) _____7. 18x³ -24x² + 3x g. 11a(1 + 2a) _____8. 2x² - 6x + 8 h. 3(x + 3y) _____9. 11a + 22a² i. 3x(6x² - 8x + 1) _____10. 24x³ - 64y² j. 3a (6a² + ab – 6b²)     Previous Next TABLE OF CONTENTS Answers
  169. 169. Answers 1. H 2. F 3. J 4. D 5. C 6. B 7. I 8. A 9. G 10. E Questions
  170. 170. Activity 39 Name: _______________________Score:_____________Date: ______________ Year and Section: _________________Teacher: __________________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to factor a polynomial out of common factor. </li></ul><ul><li>To have patience in finding a common factor of a polynomial. </li></ul><ul><li>To show the solution in finding the common a factor of a polynomial. </li></ul>Instruction: Factor the following algebraic expression. Get their common factor. Write your answer in the space provided. 1. 2ab + 8a²b²c² - 16a³b³c³ 2. 10a²y³ + 4ay 3. 2c³ - 4c² - 6c 4. 11m + 22m² 5. 12a³ - 24a² - 48a 6. 6c 4 – 8c³ - 2c² 7. 2b³ - 4b² - 8b + 10 8. 3y⁶ - 12y³ - 5y 9. 3ax² - 6a²x + 9a³x 10. 18x² - 24xy + 3y²   Previous Next TABLE OF CONTENTS Answers
  171. 171. Answers 1. 2(ab + 4a 2 b 2 c 2 – 8a 3 b 3 c 3 2. 2ay(5ay 2 + 2) 3. 2c(c 2 – 2c – 3) 4. 11m(1 + 2m) 5. 12a(a 2 – 2a – 4) 6. 2c(3c 3 – 4c 2 – c) 7. 2(b 3 - 2b 2 – 4b + 5) 8. 3y(y 5 – 4y 2 – 5) 9. 3ax(x – 2a + 3a 2) 10. 3(6x 2 – 8xy + y 2 ) Questions
  172. 172. Activity 40 Name: _______________________Score:_____________Date:__________ Year and Section: _________________Teacher: ______________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to factor a polynomial by grouping. </li></ul><ul><li>To find the factor of a polynomial by grouping. </li></ul><ul><li>To increase proficiency in factoring a polynomial by grouping. </li></ul>Instruction: Tell whether if the factor by grouping of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor.   _____1. The factor of ax + ay + bx + by is (a + b) (x + y). _____2. The factor of 2x +8y – 3px -12py is (2 – 3p) (x + 4y). _____3. The factor of 3x – 3y + 4ay – 4ax is (3 – 4a) (x – y). _____4. The factor of x³ + 7x² + 2x ² 14 is (x² + 2) ( x + 7). _____5. The factor of 3x² + xy -12x -4y is (x – 4) (3x + y). _____6. The factor of 2a²x – 8b²x + a² - 4b²y is (2x + y)(a + 2b)(a + 2b). _____7. The factor of x² + 2xy + y² - z² is (x + y + z) (x + y + z). _____8. The factor of mx² - my² + nx² -ny² is (m + n) (x + y). _____9. The factor of x² - y² + 4yz – 4z² is (x + y – z) (x – y + z). _____10. The factor of 9a⁴b³ + 15a³b² - 3a²b is (3ab + 3ab) (5ab – 1).   Previous Next TABLE OF CONTENTS Answers
  173. 173. Answers 1. A 2. A 3. A 4. A 5. A 6. B (2x + y)(a - 2b)(a + 2b) 7. B (x + y + z) (x + y - z). 8. B (m + n) (x + y) (x – y) 9. A 10. B (3a 2 b + 5ab) (3a 2 b – 1). Questions
  174. 174. Activity 41 Name:_______________________Score:_____________Date:___________ Year and Section: _________________Teacher: _______________________ <ul><li>Objectives: </li></ul><ul><li>To identify the factor of a polynomial by grouping. </li></ul><ul><li>To find the factor of a polynomial by grouping. </li></ul><ul><li>To increase proficiency in factoring a polynomial by grouping. </li></ul>Instruction: Match the polynomials in column A to its proper factor of grouping in column B . Write your answer in the space provided before each number.   A B _____1. 15x⁴ - 15x² + 5x² a. (x – 4y) (2x + 3y) _____2. 2a⁵b² + 8a⁴b³ -4a³b⁴ b. (5x + 1) (x + 2) _____3. a³ -2a² + 5a – 10 c. 5x² (x² - 3x + 1) _____4. 3xy + 21x -2y – 14 d. (3 + a) (x – 5) _____5. 5x² + 11x + 2 e. (a – 2) (a² + 5) _____6. 4x² + 7x – 15 f. (x + 4) (x -3) _____7. x³ - 3x + 4x – 12 g. (4x – 5) (x + 3) _____8. 2x² +3xy - 8xy – 12y² h. (y + 7) (3x – 2) _____9. 3x – 15 + ax – 5a i. (x + 4) (x – 6) _____10. x² - 6x + 4x – 24 j. 2a³b² (a² + 4ab - 2b²)   Previous Next TABLE OF CONTENTS Answers
  175. 175. Answers 1. C 2. J 3. E 4. H 5. B 6. G 7. F 8. A 9. D 10. I Questions
  176. 176. Activity 42 Name: ________________________Score:_____________ Date: _________ Year and Section: _________________Teacher: _______________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to factor a polynomial by grouping. </li></ul><ul><li>To have patience in finding a factor of a polynomial by grouping. </li></ul><ul><li>To show the solution in finding the factor of a polynomial by grouping. </li></ul>Instruction: Factor the following algebraic expressions by grouping. Write your answer in the space provided. 1. 27x³ + 108x² + 144x + 64 2. 4b² + 12bc + 9c² - 25d 3. 36x² - 9y² + 24yz- 16z² 4. ax² -4a + 3x² - 12 5. 36x² - 9y² + 24yz – 16z² 6. 16p² - t² + 2st - s² 7. ac + 2bc – ad – 2bd 8. 27m + 27 n – mn³ - n⁴ 9. 30mx + 18my – 10nx - 6ny 10. 4a²m + 4a²n - b²m - b²n     Previous Next TABLE OF CONTENTS Answers
  177. 177. Activity 43 Name: _______________________Score:_____________ Date:_______ Year and Section: _________________Teacher: ____________________ <ul><li>Objectives:: </li></ul><ul><li>To recall how to factor a polynomial of the difference of two squares. </li></ul><ul><li>To find the factor of difference of two squares. </li></ul><ul><li>To increase proficiency in factoring the difference of two squares. </li></ul>Instruction: Tell whether if the factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor.   _____1. The factor of m² - 144 is (m + 7) (m + 7). _____2. The factor of b²x² - y² is (b + y) (x – y). _____3. The factor of 25 - p² is (5 + p) (5 – p). _____4. The factor of 64x²y² - x² is (8xy + y) (8xy – x). _____5. The factor of c² - d⁴ is (c + d²) (c - d²). _____6. The factor of a² b² - 36x² is (a² + 6x) (b² - 6x). _____7. The factor of x⁴y⁴ - 9 is (x⁴ + 3) (y⁴ -3). _____8. The factor of 49 – a⁶ is (7 + a³) (7 - a³). _____9. The factor of 64y² - 121 is (8y + 11) (8y – 11). _____10. The factor of 9x² - 16 is (3x + 4) (3x – 4).   Previous Next TABLE OF CONTENTS Answers
  178. 178. Answers 1. B (m + 7) (m - 7) 2. B (bx + y) (xx – y) 3. A 4. B (8xy + x) (8xy – x) 5. A 6. A 7. A 8. A 9. A 10. A Questions
  179. 179. Activity 44 Name: _______________________ Score:_____________Date: _________ Year and Section: _________________Teacher: _______________________ <ul><li>Objectives: </li></ul><ul><li>To identify the factor of the difference of two squares. </li></ul><ul><li>To find the factor of the difference of two squares. </li></ul><ul><li>To increase proficiency in factoring the difference of two squares. </li></ul>  Instruction: Match polynomials in column A to its correct factoring which is the difference of two squares in column B . Write your answer in the space provided before each number.   A B _____1. x² - 9 a. (x⁴ + y⁴) (x² + y²) (x + y) (x – y) _____2. 4x² - 36y⁶ b. 4xy (2x + 3y) (2x - 3y) _____3. 49x⁴ - 36y⁴ c. (x + 3) (x – 3) _____4. x⁸ - y⁸ d. (x³ + 2) (x³ - 2) _____5. (t + 4)² - 9 e. (6x + 1) (6x – 1) _____6. 16x³y – 36xy³ f. 2 (81x⁴ - 16y⁸) _____7. 12x³ - 27xy² g. (7x² + 6y²) (7x² - 6y²) _____8. 162x⁴ - 32y⁸ h. ( t + 7) (t + 1) _____9. x⁶ - 4 i. 3x (4x² - 9y²) _____10. 36x² - 1 j. 4x² (1 + 3y²) (1 - 3y²) Previous Next TABLE OF CONTENTS Answers
  180. 180. Answers 1. C 2. J 3. G 4. A 5. H 6. B 7. I 8. F 9. D 10. E Questions
  181. 181. Activity 45 Name: _______________________Score:_____________Date: ______________ Year and Section: _________________Teacher: __________________________ <ul><li>Objectives: </li></ul><ul><li>To recall how to factor the difference of two squares. </li></ul><ul><li>To have patience in finding the factor of the difference of two squares. </li></ul><ul><li>To show the solution in finding the factor of the difference of two squares. </li></ul>Instruction: Factor the difference of the two squares of the given polynomials. Write your answer in the space provided
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