Math factoring Grade 8 Krystal, Dustine, John

1. SECOND QUARTER’s
PERFORMANCE TASK:
FACTORING
ICL: Showcase of Solution and Final Answer

2. Group Name: _CYCLOID____
Second Quarter Grade 8 Mathematics Performance Task Factoring 2
KRYSTAL MIZONA
DUSTINE DANAE V. VILLA
CARLO TORRES
NAME OF STUDENT 4

3. Krystal Anne V. Mizona
Second Quarter Grade 8 Mathematics Performance Task Factoring 3
Insert Picture
Here
GCMF
BINOMIAL
•DTS
•STC
•DTC
QUADRATIC TRINOMIALS
•PST
•QT 1
•QT 2
•GQT
Factoring by GROUPING / Factoring
COMPETELY

4. Name:
GREATEST COMMON MONOMIAL FACTOR (GCMF)
• QUESTION 1:
• 6y + 4y2
• GCF: 2y
Solution:
2y ÷ 6y = 3y
2y ÷ 2y2 = y
Answer:
2y (3y + y)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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5. Name:
GREATEST COMMON MONOMIAL FACTOR (GCMF)
• QUESTION 2:
• 9jk4 + 15i + 12y
GCF: 3
Solution:
3 ÷ 9jk4 = 3k3
3 ÷ 15i = 5
3 ÷ 12y = 4
Answer: 3 (3k3 + 5 + 4)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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6. Name:
DIFFERENCE OF TWO SQUARES (DTS)
• QUESTION 1:
• x2 - 16k4
Solution:
√x2 = x
√-16k4 = -4k2 & 4k2
Answer:
=(x + 4k2) (x - 4k2)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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7. Name:
DIFFERENCE OF TWO SQUARES (DTS)
• QUESTION 2:
• 16s2 - 576k4
Solution:
√16s2 = 4s
√-576k4 = -24k2 & 24k2
Answer:
=(4s + 24k2) (4s - 24k2)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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8. Name:
SUM OF TWO CUBES (STC)
• QUESTION 1:
• 216m9 + 27o6
Solution: Binomial Factor
3√216m9 = 6m3
3√27o6 = 3o2
Answer: (6m3 + 3o2)3
Trinomial Factor:
(6m3 + 3o2)2 = (36m6 + 18m3o2 + 9o4)
Final Answer: (6m3 + 3o2) (36m6 + 18m3o2 + 9o4)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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9. Name:
SUM OF TWO CUBES (STC)
• QUESTION 2:
• 512s15 + 729i6
Solution: Binomial Factor
3√512s15 =8s5
3√-729i6 =9i2
Answer= (8s5 + 9i2)3
Trinomial Factor
Answer: (8s5 + 9i2)2 = (64s10 + 72s5i2 + 81i4)
Final Answer: (8s5 + 9i2) (64s10 + 72s5i2 + 81i4)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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10. Name:
DIFFERENCE OF TWO CUBES (DTC)
• QUESTION 1:
• 64n3 - 125m12
Solution: Binomial Factor
3√64n3 =4n
3√-125m12 =-5m4
Answer: (4n - 5m4)3
Trinomial Factor:
(4n - 5m4)2 = (16n2 - 20nm4 + 25m8)
Final Answer: (4n - 5m4) (16n2 - 20nm4 + 25m8)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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11. Name:
DIFFERENCE OF TWO CUBES (DTC)
• QUESTION 2:
• 1728y21 - 5832h27
Solution: Binomial Factor:
3√1728y21 =12y7
3√-5832h27 =-18h9
Answer: (12y7 - 18h9)3
Trinomial Factor:
(12y7 - 18h9)2 = (144y14 - 216y7h9 + 324h18)
Final Answer: (12y7 - 18h9) (144y14 - 216y7h9 + 324h18)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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12. Name:
PERFECT SQUARE TRINOMIAL (PST)
• QUESTION 1:
• x2 + 8xk + 12k2
Solution:
√x2
√12k2
Answer:
=(x + 4k)2
Second Quarter Grade 8 Mathematics Performance Task Factoring
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13. Name:
PERFECT SQUARE TRINOMIAL (PST)
• QUESTION 2:
• x2 + 24xy2 + 144y4
Solution:
√x2 = x
√144y4 = 12y2
Answer:
=(x + 12y2)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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14. Name:
Quadratic Trinomial in the form: ax2 + bx + c
where a = 1 and c is POSITIVE (QT1)
• QUESTION 1:
• x2 + 41 + 210
Solution:
AC TEST
Answer:
(x + 35) (x + 6)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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41 6
35210

15. Name:
Quadratic Trinomial in the form: ax2 + bx +
c where a = 1 and c is POSITIVE (QT1)
• QUESTION 2:
• j2 + 68 + 867
Solution:
Answer:
(j + 17) (j + 51)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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867
68 51
17

16. Name:
Quadratic Trinomial in the form: ax2 + bx + c
where a = 1 and c is NEGATIVE (QT2)
• QUESTION 1:
•x2 + 20 - 125
Solution:
Answer:
(x + 25) (x - 5)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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-125
20 -5
25

17. Name:
Quadratic Trinomial in the form: ax2 + bx + c
where a = 1 and c is NEGATIVE (QT2)
• QUESTION 2:
• a2 + 27 - 90
Solution:
AC TEST
Answer:
(a + 30) (a - 3)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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-90
27 -3
30

18. Name:
GENERAL QUADRATIC TRINOMIAL (GQT)
• QUESTION 1:
• 2o2 + 13 + 15
Solution:
Answer:
(o2 + 5) (o2 + 3)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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30 10
313
10
2
3
2
=5 =3
AC TEST

19. • QUESTION 2:
• 2i2 -17 + 15
Solution:
Answer:
(i2 - 15) (i2 - 2)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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Name:
GENERAL QUADRATIC TRINOMIAL (GQT)
30 -15
-17 -2
AC TEST

20. Name:
FACTORING BY GROUPING
• QUESTION 1:
• x2 + 2x + yx + 2y
Solution:
GCMF: x (x + 2)
GCMF: y (x + 2)
Answer:
(x + 2) (x + y)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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21. Name:
FACTORING COMPLETELY
Second Quarter Grade 8 Mathematics Performance Task Factoring
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• QUESTION 1: n2 + 4n + 2 - v4
SOLUTION:
PST: n2 + 4n + 2
= (n + 2)2
DTS: (n + 2)2 - v4
= [(n + 2)2- v2] [(n + 2)2- v2]
FINAL ANSWER:
[(n + 2)2- v2] [(n + 2)2- v2]

22. DUSTINE VILLA
Second Quarter Grade 8 Mathematics Performance Task Factoring 22
Insert Picture
Here
GCMF
BINOMIAL
•DTS
•STC
•DTC
QUADRATIC TRINOMIALS
•PST
•QT 1
•QT 2
•GQT
Factoring by GROUPING / Factoring
COMPETELY

23. DUSTINE DANAE V. VILLA
GREATEST COMMON MONOMIAL
FACTOR (GCMF)
• QUESTION 1:
10x + 6x
GCF: 2x
SOLUTION:
2x/10x =5
2x/6x =3
FINAL ANSWER:
2x (5 + 3)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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24. DUSTINE DANAE V. VILLA
GREATEST COMMON MONOMIAL
FACTOR (GCMF)
• QUESTION 2:
• 20c4 - 40c3z2 + 60cz2
GCF: 20c
SOLUTION:
20c/20c4 = c3
20c/-40c3z2 = -2c2z2
20c/60c = 3
FINAL ANSWER:
20c (c3 - 2c2z2 + 3z2)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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25. DUSTINE DANAE V. VILLA
DIFFERENCE OF TWO SQUARES
(DTS)
• QUESTION 1: 16v4 - 25d2n4
SOLUTION:
√16v4 = 4v2 (principal root)
√-25d2n4 = 5dn2 and -5dn2 (+/- root)
FINAL ANSWER:
(4v2 + 5dn2) (4v2 - 5dn2 )
Second Quarter Grade 8 Mathematics Performance Task Factoring
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26. DUSTINE DANAE V. VILLA
DIFFERENCE OF TWO SQUARES
(DTS)
• QUESTION 2: 144x10v2 - 121d6n4
SOLUTION:
√144x10v2 = 12x5v (principal root)
√-121d6n4 = 11d3n2 (+/- root)
FINAL ANSWER:
( 12x5v + 11d3n2 ) (12x5v - 11d3n2 )
Second Quarter Grade 8 Mathematics Performance Task Factoring
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27. DUSTINE DANAE V. VILLA
SUM OF TWO CUBES (STC)
• QUESTION 1: 8x15 + 27n12
SOLUTION:
BINOMIAL FACTORS:
∛8x15 = 2x5
∛27n12 = 3n4
TRINOMIAL FACTORS:
(2x5)2 -(2x5)(3n4) + (3n4)2
FINAL ANSWER:
(2x5 + 3n4) (4x10 - 6x5n4 + 9n8)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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28. DUSTINE DANAE V. VILLA
SUM OF TWO CUBES (STC)
• QUESTION 2: 64d21 + 125n12
SOLUTION:
BINOMIAL FACTORS:
∛64d21 = 4d7
∛125n12 = 5n4
TRINOMIAL FACTORS:
(4d7)2 -(4d7)(5n4) + (5n4)2
FINAL ANSWER:
(4d7 + 5n4) (16d14 - 20d5n4 + 25n8)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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29. DUSTINE DANAE V. VILLA
DIFFERENCE OF TWO CUBES
(DTC)
• QUESTION 1: 8c21 - 27v12
SOLUTION:
BINOMIAL FACTORS:
∛8c21 = 2c7
∛27v12 = 3v4 = -(3v4)
TRINOMIAL FACTORS:
(2c7)2 + (2c7)(3v4) + (3v4)2
FINAL ANSWER:
(2c7 - 3v4) (4c14 + 6c7v4 + 9v8)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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30. DUSTINE DANAE V. VILLA
DIFFERENCE OF TWO CUBES
(DTC)
• QUESTION 2: 64r24 + 216a30
SOLUTION:
BINOMIAL FACTORS:
∛64r24 = 4r8
∛216a30 = 6a10 = -(6a10 )
TRINOMIAL FACTORS:
(4r8)2 (4r8)(6a10 ) + (6a10 )2
FINAL ANSWER:
(4r8 - 6a10 ) (16r16 + 24r8a10 + 36a10)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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31. DUSTINE DANAE V. VILLA
PERFECT SQUARE TRINOMIAL
(PST)
• QUESTION 1: v2 + 8vx + 16x2
SOLUTION:
√v2 = v
√16x2 = 4x
FINAL ANSWER:
(V + 4x)2
Second Quarter Grade 8 Mathematics Performance Task Factoring
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32. DUSTINE DANAE V. VILLA
PERFECT SQUARE TRINOMIAL
(PST)
• QUESTION 2: 4v4 - 12v2n2 + 9n4
SOLUTION:
√4v4 = 2v2
√9n4 = 3n2
FINAL ANSWER:
(2v2 - 3n2)2
Second Quarter Grade 8 Mathematics Performance Task Factoring
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33. NAME:
QUADRATIC TRINOMIAL IN THE FORM:
AX2 + BX + C WHERE A = 1 AND C IS
POSITIVE (QT1)
• QUESTION 1: v2 + 11v + 30
SOLUTION:
AC TEST
√v2 = v
FACTORS OF THE THIRD TERM: 5 & 6
FINAL ANSWER:
(v+5)(v+6)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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30 5
11 6
DUSTINE DANAE V.
VILLA

34. NAME:
QUADRATIC TRINOMIAL IN THE
FORM: AX2 + BX + C WHERE A = 1 AND
C IS POSITIVE (QT1)
• QUESTION 2: c2 - 6c + 40
SOLUTION:
AC TEST
√c2= c
FACTORS OF THE THIRD TERM: 10 & -4
FINAL ANSWER:
(c+10)(c-4)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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40 10
6 -4
DUSTINE DANAE V. VILLA

35. DUSTINE DANAE V. VILLA
QUADRATIC TRINOMIAL IN THE FORM: AX2 +
BX + C WHERE A = 1 AND C IS NEGATIVE
(QT2)• QUESTION 1: r2 + 6r - 55
SOLUTION:
AC TEST
√r2= r
FACTORS OF THE THIRD TERM: 11 & -5
FINAL ANSWER:
(r+11)(r-5)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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-55 11
6 -5

36. DUSTINE DANAE V. VILLA:
QUADRATIC TRINOMIAL IN THE FORM: AX2 +
BX + C WHERE A = 1 AND C IS NEGATIVE (QT2)
• QUESTION 2: j2 - 15j -100
SOLUTION:
AC TEST
√r2= j
FACTORS OF THE THIRD TERM: -20 & 5
FINAL ANSWER:
(r -20)(r+5)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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-100 -20
-15 5

37. DUSTINE DANAE V. VILLA
GENERAL QUADRATIC TRINOMIAL
(GQT)
• QUESTION 1: 2x2 + 5x + 7
SOLUTION:
AC TEST = FRACTIONS: 2/7 & 2/-2
=SIMPLIFIED FORM: 2/7 & 1/-1
FINAL ANSWER:
(2x + 7) (x-1) 2/2/15 2/-2 = (simplified) 2/15 1/-1
15 2/-2 = (simplified) 2/15 1/-1
2/15 2/-2 = (simplified) 2/15 1/-1
Second Quarter Grade 8 Mathematics Performance Task Factoring
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-14 7
5 -2

38. • QUESTION 2: FACTOR 4r^2 – 5 -9
SOLUTION:
AC TEST = FRACTIONS: 4/-9 & 4/-4
=SIMPLIFIED FORM: 4/-9 & 1/-1
FINAL ANSWER:
(4r - 9) (x+1) 2/2/15 2/-2 = (simplified) 2/15 1/-1
15 2/-2 =
Second Quarter Grade 8 Mathematics Performance Task Factoring
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DUSTINE DANAE V. VILLA
GENERAL QUADRATIC TRINOMIAL
(GQT)
-36 -9
-5 4

39. DUSTINE DANAE V. VILLA
FACTORING BY GROUPING
• QUESTION 1: ca + ja - jy - cy
SOLUTION: GCMF
• (ca - cy) + ( ja - jy)
GCMF: c ( a-y) + j ( a -y)
GCMF: (a-y) (c+j)
FINAL ANSWER:
( a - y )( c + y )
Second Quarter Grade 8 Mathematics Performance Task Factoring
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40. DUSTINE DANAE V. VILLA
FACTORING COMPLETELY
• QUESTION 1: n2 + 4n + 2 - v4
SOLUTION:
PST: n2 + 4n + 2
= (n + 2)2
DTS: (n + 2)2 - v4
= [(n + 2)2- v2] [(n + 2)2- v2]
FINAL ANSWER:
[(n + 2)2- v2] [(n + 2)2- v2]
Second Quarter Grade 8 Mathematics Performance Task Factoring
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41. REFLECTION
Group Name ____
1 2
3 4

42. Krystal Mizona
I IMPROVED AND UNDERSTAND THE TOPICS IN
FACTORING, BUT SOMETIMES I EASILY FORGET HOW AM I
GOING TO FACTOR OR SOLVE SOME QUESTIONS.
HONESTLY SOMETIMES WHEN I CREATE A QUESTION I
PUT THE ANSWERS FIRST THAN THE ONE THAT IM GOING
TO FACTOR BECAUSE I COULDN’T THINK OF ANY
QUESTION.
Second Quarter Grade 8 Mathematics Performance Task Factoring 42
1 2
3 4

43. DUSTINE DANAE V. VILLA
I HAVE LEARNED AND MASTERED THE DIFFERENT FACTORING TECHNIQUES
THROUGH THIS PETA AND AT THE SAME TIME I COULD HELP OTHER STUDENTS
LIKE ME IF THEY HAVE MISCONCEPTIONS, ETC. I ALSO FULLY UNDERSTAND THAT
I COULD HELP OTHER PEOPLE THROUGH THIS WEBSITES OR GOOGLE FORMS AND
ELEAP AND I COULD REACH OUT TO THEM WITHOUT ANY COST. I HAVE LEARNED
TO HELP WITHOUT WASTING THROUGH THIS PAPERLESS PETA. I HAVE FULLY
UNDERSTAND THE TRUE MEANING OF TEAMWORK AND IT IS IMPORTANT TO
HELP AND COMMUNICATE ON ANOTHER TO ACHIEVE YOUR GOALS. I ALSO
LEARNED THAT NOTHING WOULD BE HARD IF WE ONLY WORK TOGETHER. I
LOOK FORWARD TO MORE PETAS LIKE THIS.
Second Quarter Grade 8 Mathematics Performance Task Factoring 43
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3 4