Happy Math Humans (group h) of 8 - St. Basil
3 students of 8 - St. Basil representing the group Happy Math Humans, will show you how to factor different types of polynomials.
2. Group Name: Happy Math Humans
Second Quarter Grade 8 Mathematics Performance Task Factoring 2
Andrea Marie S. Alarcon
Rico Dizon
Bianca Roque
NAME OF STUDENT 4
3. Andrea Marie S. Alarcon
Second Quarter Grade 8 Mathematics Performance Task Factoring 3
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GCMF
BINOMIAL
â˘DTS
â˘STC
â˘DTC
QUADRATIC TRINOMIALS
â˘PST
â˘QT 1
â˘QT 2
â˘GQT
Factoring by GROUPING / Factoring
COMPETELY
4. Name:
GREATEST COMMON MONOMIAL FACTOR (GCMF)
⢠QUESTION 1: 8x2 + 4xy
Solution:
1)Find the greatest monomial factor (GCMF): 4x
2)Divide the polynomial by the GCMF. The quotient is the factor
3)Express the polynomial as the product of the quotient and the
GCMF
Final Answer: 4x (2x + y)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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5. Name:
GREATEST COMMON MONOMIAL FACTOR (GCMF)
⢠QUESTION 2: 10x2y4 + 8x2y
Solution:
1)Find the greatest monomial factor (GCMF): 4x2y
2)Divide the polynomial by the GCMF. The quotient is the factor
3)Express the polynomial as the product of the quotient and the
GCMF
Final Answer: 2x2y (5y3 + 4)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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6. Name:
SUM OF TWO CUBES (STC)
⢠QUESTION 1: 64b3 + 27
Solution:
1)find the cube roots of each term. The quotients will be the
binomial: (4b + 3)
(For the trinomial)
1)Square the first term of the binomial: 16b2
2)Opposite the product of the terms inside the binomial: -12b
3)Square the last term of the binomial: 9
Final Answer: (4b + 3)(16b2 - 12b + 9)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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7. Name:
SUM OF TWO CUBES (STC)
⢠QUESTION 2: 64x3 + 8z3
Solution:
1)find the cube roots of each term. The quotients will be the
binomial: (4x + 2z)
(For the trinomial)
1)Square the first term of the binomial: 16x2
2)Opposite the product of the terms inside the binomial: -8xz
3)Square the last term of the binomial: 4
Final Answer: (4x + 2z)(16x2 - 8xz + 4)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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8. Name:
DIFFERENCE OF TWO CUBES (DTC)
⢠QUESTION 1: 27b3 - 8z3
Solution:
1)find the cube roots of each term. The quotients will be the
binomial: (3b - 2z)
(For the trinomial)
1)Square the first term of the binomial: 9b2
2)Opposite the product of the terms inside the binomial: +6bz
3)Square the last term of the binomial: 4z2
Final Answer = (3b - 2z)(9b2 + 6bz + 4z2)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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9. Name:
DIFFERENCE OF TWO CUBES (DTC)
⢠QUESTION 2: 343a3 - 125b3
Solution:
1)find the cube roots of each term. The quotients will be the
binomial: (7a - 5b)
(For the trinomial)
1)Square the first term of the binomial: 49a2
2)Opposite the product of the terms inside the binomial: 35ab
3)Square the last term of the binomial: 25b2
Final Answer: (7a - 5b)(49a2 + 35ab + 25b2)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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10. Name:
PERFECT SQUARE TRINOMIAL (PST)
⢠QUESTION 1: x2 - 12x + 36
Solution:
1)Find the square root of the first term: x
2)Find the square root of the last term and copy the sign of the
middle term: -6
= (x - 6)(x - 6)
Final Answer: (x - 6)2
Second Quarter Grade 8 Mathematics Performance Task Factoring
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11. Name:
PERFECT SQUARE TRINOMIAL (PST)
⢠QUESTION 2: x2 + 10x + 25
Solution:
1)Find the square root of the first term: x
2)Find the square root of the last term and copy the sign of the
middle term: -6
= (x + 5)(x + 5)
Final Answer (x + 5)2
Second Quarter Grade 8 Mathematics Performance Task Factoring
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12. Name:
Quadratic Trinomial in the form: ax2 + bx + c
where a = 1 and c is POSITIVE (QT1)
⢠QUESTION 1: x2 + 7x + 12
Solution:
1)Find the square root of the first term: x
2)Find the factors of the last term that will result to the middle
term: 4, 3
Final Answer: (x + 4)(x + 3)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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13. Name:
Quadratic Trinomial in the form: ax2 + bx +
c where a = 1 and c is POSITIVE (QT1)
⢠QUESTION 2: x2 + 6 + 8
Solution:
1)Find the square root of the first term: x
2)Find the factors of the last term that will result to the middle
term: 4, 2
Final Answer: (x + 4)(x + 2)
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 NEGATIVE (QT2)
⢠QUESTION 1: x2 + 7x - 18
Solution:
1)Find the square root of the first term: x
2)Find the factors of the last term that will result to the middle
term: 9, -2
Final Answer: (x + 9)(x - 2)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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15. Name:
Quadratic Trinomial in the form: ax2 + bx + c
where a = 1 and c is NEGATIVE (QT2)
⢠QUESTION 2: x2 + 3x - 18
Solution:
1)Find the square root of the first term: x
2)Find the factors of the last term that will result to the middle
term: 6, -3
Final Answer: (x + 6)(x - 3)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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16. Name:
GENERAL QUADRATIC TRINOMIAL (GQT)
⢠QUESTION 1: 5x2 + x - 4
Solution:
â˘find the factors of the first and last terms that will add up to the
middle coefficient 1: 5, -4
â˘replace x with 5x - 4x (notice 5x - 4x adds up to x. So it is equivalent
to x): 5x2 + 5x - 4x - 4
3) factor by grouping and group the first two terms then the last two
terms: (5x2 + 5x)(-4x - 4)
4) find the GCF of the first group and factor: 5x (x + 1) 4)
5)find the GCF of the second group and factor: -4 (x + 1)
6) group like terms: (4x - 3)(x + 1)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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17. ⢠QUESTION 2: 4x2 + x - 3
Solution:
1) find the factors of the first and last terms that will add up to the
middle coefficient 1: 4, -3
2) replace x with 4x - 3x (notice 4x - 3x adds up to x. So it is
equivalent to x): 4x2 + 4x - 3x - 3
3) factor by grouping
4) find the GCF of both groups: 4x (x + 1) -3 (x + 1)
5) group like terms: (4x - 3)(x + 1)
Second Quarter Grade 8 Mathematics Performance Task Factoring
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Name:
GENERAL QUADRATIC TRINOMIAL (GQT)
18. Name:
FACTORING BY GROUPING 18
Second Quarter Grade 8 Mathematics Performance Task Factoring
⢠QUESTION 1: 4x3 + 9x2 + 4x + 9
Solution:
1)group like terms: (4x3 + 4x)
2)then group the last two remaining terms: (9x2 + 9)
3)factor out the gcf of both groups and factor: 4x (x2 + 1) +
9 (x2 + 1)
1)combine the GCFs and like terms: (x2 + 1)(2x + 7)
19. Name:
FACTORING COMPLETELY
⢠QUESTION 1: 2x2 - 28x + 98
1)Before trying any other factoring technique, try the GCMF:
2 (x2 - 14x + 49)
Solution:
Factor the remaining factorable terms inside the parenthesis
with the right factoring technique according to their type of
polynomial: 2 (x - 7)2, since it could no longer be factored, this is
the final answer.
Second Quarter Grade 8 Mathematics Performance Task Factoring
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31. NAME:
QUADRATIC TRINOMIAL IN THE FORM: AX2 +
BX + C WHERE A = 1 AND C IS POSITIVE
(QT1)
⢠QUESTION 1:
Second Quarter Grade 8 Mathematics Performance Task Factoring
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32. NAME:
QUADRATIC TRINOMIAL IN THE FORM:
AX2 + BX + C WHERE A = 1 AND C IS
POSITIVE (QT1)
⢠QUESTION 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
NEGATIVE (QT2)⢠QUESTION 1:
Second Quarter Grade 8 Mathematics Performance Task Factoring
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34. NAME:
QUADRATIC TRINOMIAL IN THE FORM:
AX2 + BX + C WHERE A = 1 AND C IS
NEGATIVE (QT2)⢠QUESTION 2:
Second Quarter Grade 8 Mathematics Performance Task Factoring
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40. Name:
GREATEST COMMON MONOMIAL FACTOR (GCMF)
⢠QUESTION 1: 4y^2+12xy
⢠Solution:
⢠Find the greatest monomial factor (GCMF): 4y
⢠Divide the polynomial by the GCMF the quotient is the factor.
⢠Express the polynomial as the product of the quotient and the
GCMF
Answer: 4y(y+3x)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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41. Name:
GREATEST COMMON MONOMIAL FACTOR (GCMF)
⢠QUESTION 2: 4y^2x^4+14x
⢠Solution:
⢠Find the greatest monomial factor (GCMF): 2x^2y
⢠Divide the polynomial by the GCMF the quotient is the factor.
⢠Express the polynomial as the product of the quotient and the
GCMF
Answer: 2x^2y(2y+7)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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42. Name:
DIFFERENCE OF TWO SQUARES (DTS)
⢠QUESTION 2: (121a^2b^8-4c^6d^2)
Solution:
(11a)^2-(4c)^2
Answer: (11a+4c)(11a-4c)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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44. Name:
SUM OF TWO CUBES (STC)
⢠QUESTION 1: 27a^3+8
⢠Solution:
⢠Find the cube roots of the each term. The quotients will be the
binomial: (3a+2)
⢠Square the first term of the binomial: 9a^2
⢠Opposite the product of the terms inside the binomial:
⢠Square the last term of the binomial:
Answer: (3a+2)(9a^2-6a+4)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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45. Name:
SUM OF TWO CUBES (STC)
⢠QUESTION 2: 27a^3+64y^3
⢠Solution:
⢠Find the cube roots of the each term. The quotients will be the
binomial: (3a+4y)
⢠Opposite the product of the terms inside the binomial:
⢠Square the last term of the binomial:
Answer: (3a+2)(9a^2-6a+4)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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46. Name:
DIFFERENCE OF TWO CUBES (DTC)
⢠QUESTION 1: 64y^3 - 27a^3
⢠Solution:
⢠Find the cube roots of the each term the quotients will be the
binomial: (4y-3a)
⢠Opposite the product of the terms inside the binomial:
⢠Square the last term of the binomial:
Answer: (4y-3a)(16^2+12ay+9a^2)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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47. Name:
DIFFERENCE OF TWO CUBES (DTC)
⢠QUESTION 2: 125y^3 - 64^3
⢠Solution:
⢠Find the cube roots of the each term the quotients will be the
binomial: (5y-4a)
⢠Square the first term of the binomial:
⢠Opposite the product of the terms inside the binomial:
⢠Square the last term of the binomial:
Answer: (5y-4a)(25^2+20ay+16a^2)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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48. Name:
PERFECT SQUARE TRINOMIAL (PST)
⢠QUESTION 1: x^2+16x+25
Solution:
1) Find the square root of the first term: x
2) Find the square root of the last term and copy the sign of the
middle term: 25y^2 = 5y
Answer: (x+5y)^2
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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49. Name:
PERFECT SQUARE TRINOMIAL (PST)
⢠QUESTION 2: 4a^2 - 25ab + 36ab^2
⢠Solution:
⢠1) Find the square root of the first term: 2a
⢠2) Find the square root of the last term and copy the sign of the
middle term: 36^2 = 6b
Answer: (2a-6b)^2
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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50. Name:
Quadratic Trinomial in the form: ax2 + bx +
c where a = 1 and c is POSITIVE (QT1)
⢠QUESTION 1: a^2 - 8a + 12
⢠Solution:
⢠1) Find the square root of the first term: a
⢠2) Find the square root of the last term and copy the sign of the
middle term: -4 and -3
Answer: (a-4)(a-3)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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51. Name:
Quadratic Trinomial in the form: ax2 +
bx + c where a = 1 and c is POSITIVE
(QT1)
⢠QUESTION 2: a^2 - 12a + 16
⢠Solution:
⢠Find the square root of the first term: a
⢠Find the square root of the last term and copy the sign of the
middle term: -4 and -4
Answer: (a-4)(a-4)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
51
52. Name:
Quadratic Trinomial in the form: ax2 + bx + c
where a = 1 and c is NEGATIVE (QT2)⢠QUESTION 1: a^2 + 12a - 36
⢠Solution:
⢠Find the square root of the first term: a
⢠Find the factors of the last term that will result to the middle term:
6 and -6
Answer: (a+6)(a-6)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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53. Name:
Quadratic Trinomial in the form: ax2 + bx + c
where a = 1 and c is NEGATIVE (QT2)⢠QUESTION 2: x^2+ 8x - 16
⢠Solution:
⢠Find the square root of the first term: x
⢠Find the factors of the last term that will result to the middle
term:4 and -4
Answer: (x+4)(x-4)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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56. Name:
FACTORING BY GROUPING
⢠QUESTION 1: 2x^3 + 4x^2 + 2x + 4
1) Group the first 2 terms: (2x^3+4x^2)
2) Group the last term two terms: (2x+4)
3) Factor out the gcf of both groups:
4) combine like terms
Answer: 2(3x^2+x+2)
Second Quarter Grade 8
Mathematics Performance
Task Factoring
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69. Name:
Quadratic Trinomial in the form: ax2 +
bx + c where a = 1 and c is POSITIVE
(QT1)⢠QUESTION 1:
Second Quarter Grade 8 Mathematics
Performance Task Factoring 69
70. Name:
Quadratic Trinomial in the form: ax2
+ bx + c where a = 1 and c is
POSITIVE (QT1)⢠QUESTION 2:
Second Quarter Grade 8 Mathematics
Performance Task Factoring 70
71. Name:
Quadratic Trinomial in the form: ax2 + bx +
c where a = 1 and c is NEGATIVE (QT2)
⢠QUESTION 1:
Second Quarter Grade 8 Mathematics
Performance Task Factoring 71
72. Name:
Quadratic Trinomial in the form: ax2 + bx +
c where a = 1 and c is NEGATIVE (QT2)
⢠QUESTION 2:
Second Quarter Grade 8 Mathematics
Performance Task Factoring 72
78. Andrea Marie S. Alarcon
Iâve realized that making your own questions and answering them helps one
become familiar to different types of trinomials, binomials, and factoring
strategies because, I, myself, have become familiar to them.
Second Quarter Grade 8 Mathematics Performance Task Factoring 78
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80. Bianca Roque
Iâve learned that in order to factor out an expression, you must be able to
master the special products. Paying attention to your teacher is the best way
to understand the topic.
Second Quarter Grade 8 Mathematics Performance Task Factoring 80
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3 4