Factoring Strategies

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

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

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Here
GCMF
BINOMIAL
•DTS
•STC
•DTC
QUADRATIC TRINOMIALS
•PST
•QT 1
•QT 2
•GQT
Factoring by GROUPING / Factoring
COMPETELY

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
4

Name:
• 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)
5

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)
6

Name:
• QUESTION 2: 64x3 + 8z3
Solution:
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)
7

Name:
DIFFERENCE OF TWO CUBES (DTC)
• QUESTION 1: 27b3 - 8z3
Solution:
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)
8

Name:
• QUESTION 2: 343a3 - 125b3
Solution:
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)
9

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
10

Name:
• QUESTION 2: x2 + 10x + 25
Solution:
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
11

Name:
Quadratic Trinomial in the form: ax2 + bx + c
where a = 1 and c is POSITIVE (QT1)
• QUESTION 1: x2 + 7x + 12
Solution:
2)Find the factors of the last term that will result to the middle
term: 4, 3
Final Answer: (x + 4)(x + 3)
12

Name:
Quadratic Trinomial in the form: ax2 + bx +
c where a = 1 and c is POSITIVE (QT1)
• QUESTION 2: x2 + 6 + 8
Solution:
term: 4, 2
Final Answer: (x + 4)(x + 2)
13

Name:
where a = 1 and c is NEGATIVE (QT2)
• QUESTION 1: x2 + 7x - 18
Solution:
term: 9, -2
Final Answer: (x + 9)(x - 2)
14

Name:
where a = 1 and c is NEGATIVE (QT2)
• QUESTION 2: x2 + 3x - 18
Solution:
term: 6, -3
Final Answer: (x + 6)(x - 3)
15

Name:
GENERAL QUADRATIC TRINOMIAL (GQT)
• QUESTION 1: 5x2 + x - 4
Solution:
•find the factors of the first and last terms that will add up to the
middle coefficient 1: 5, -4
•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)
16

• 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)
17
Name:

Name:
FACTORING BY GROUPING 18
• 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)

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.
19

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Here
GCMF
BINOMIAL
•DTS
•STC
•DTC
•PST
•QT 1
•QT 2
•GQT
COMPETELY
Rico Dizon

NAME:
GREATEST COMMON MONOMIAL
FACTOR (GCMF)
• QUESTION 1: 3x2+ 24x + 9
Solution : GCF = 3 3(x2 + 8x + 3)
Answer : 3 (x2 + 8x + 3)
21

NAME:
FACTOR (GCMF)
• QUESTION 2: (2n3 + 6n2 + 10n)
Solution : GCF : 2n = 2n(2n3 + 3n + 5n)
Answer : 2n (2n3 + 3n + 5n)
22

NAME:
DIFFERENCE OF TWO SQUARES
(DTS)
• QUESTION 1: (x3 + 2)(x3 − 2)
Solution : (x3 + 2)(x3 − 2) = x6 − 4
Answer : x6 - 4
23

NAME:
(DTS)
• QUESTION 2: (6x − 1)(6x + 1)
Solution : (6x − 1)(6x + 1) = 36x2 − 1
Answer : 36x2 − 1
24

NAME:
• QUESTION 1:
25

NAME:
• QUESTION 2:
26

NAME:
• QUESTION 1:
27

NAME:
• QUESTION 2:
28

NAME:
• QUESTION 1:
29

NAME:
• QUESTION 2:
30

NAME:
QUADRATIC TRINOMIAL IN THE FORM: AX2 +
BX + C WHERE A = 1 AND C IS POSITIVE
(QT1)
• QUESTION 1:
31

NAME:
QUADRATIC TRINOMIAL IN THE FORM:
AX2 + BX + C WHERE A = 1 AND C IS
POSITIVE (QT1)
• QUESTION 2:
32

NAME:
NEGATIVE (QT2)• QUESTION 1:
33

NAME:
NEGATIVE (QT2)• QUESTION 2:
34

NAME:
• QUESTION 1:
35

• QUESTION 2:
36
Name:

NAME:
FACTORING BY GROUPING
• QUESTION 1:
37

NAME:
• QUESTION 1:
38

Bianca Roque
Insert Picture
Here
GCMF
BINOMIAL
•DTS
•STC
•DTC
•PST
•QT 1
•QT 2
•GQT
COMPETELY

Name:
• 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
40

Name:
• 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)
Task Factoring
41

Name:
DIFFERENCE OF TWO SQUARES (DTS)
• QUESTION 2: (121a^2b^8-4c^6d^2)
Solution:
(11a)^2-(4c)^2
Answer: (11a+4c)(11a-4c)
Task Factoring
42

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43
DIFFERENCE OF TWO SQUARES (DTS)
Question: (81a^2-25b^2)
Solution:
(9a)^2-(5b)^2
Answer: (9a+5b)(9a-5b)

Name:
• 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)
Task Factoring
44

Name:
• QUESTION 2: 27a^3+64y^3
• Solution:
• Find the cube roots of the each term. The quotients will be the
binomial: (3a+4y)
Answer: (3a+2)(9a^2-6a+4)
Task Factoring
45

Name:
• QUESTION 1: 64y^3 - 27a^3
• Solution:
• Find the cube roots of the each term the quotients will be the
binomial: (4y-3a)
Answer: (4y-3a)(16^2+12ay+9a^2)
Task Factoring
46

Name:
• 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:
Answer: (5y-4a)(25^2+20ay+16a^2)
Task Factoring
47

Name:
• 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
Task Factoring
48

Name:
• 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
Task Factoring
49

Name:
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)
Task Factoring
50

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)
Task Factoring
51

Name:
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)
Task Factoring
52

Name:
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)
Task Factoring
53

Name:
• QUESTION 1: 2x^2+11+5
Solution: (2x+1) (x+5) = 11x
Answer: 11x
Task Factoring
54

• QUESTION 2: 2x^2+ 13x + 15
Solution: (2x+3)(x+5) = 13x
Answer: 13x
Task Factoring
55
Name:

Name:
• 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)
Task Factoring
56

Name:
• QUESTION 1: 6a+8a+6b+8b
Gcmf Gcmf
6a+6b 8a+8b
=6 =8
6(a+b) 8(a+b)
Answer: (a+b)(6+8)
Task Factoring
57

NAME OF STUDENT 1
Insert Picture
Here
GCMF
BINOMIAL
•DTS
•STC
•DTC
•PST
•QT 1
•QT 2
•GQT
COMPETELY

Name:
FACTOR (GCMF)
• QUESTION 1:
Second Quarter Grade 8 Mathematics
Performance Task Factoring 59

Name:
FACTOR (GCMF)
• QUESTION 2:

Name:
(DTS)
• QUESTION 1:

Name:
(DTS)
• QUESTION 2:

Name:
• QUESTION 1:

Name:
• QUESTION 2:

Name:
DIFFERENCE OF TWO CUBES
(DTC)
• QUESTION 1:

Name:
DIFFERENCE OF TWO CUBES
(DTC)
• QUESTION 2:

Name:
• QUESTION 1:

Name:
• QUESTION 2:

Name:
Quadratic Trinomial in the form: ax2 +
bx + c where a = 1 and c is POSITIVE
(QT1)• QUESTION 1:

Name:
Quadratic Trinomial in the form: ax2
+ bx + c where a = 1 and c is
POSITIVE (QT1)• QUESTION 2:

Name:
c where a = 1 and c is NEGATIVE (QT2)
• QUESTION 1:

Name:
c where a = 1 and c is NEGATIVE (QT2)
• QUESTION 2:

Name:
GENERAL QUADRATIC TRINOMIAL
(GQT)
• QUESTION 1:

• QUESTION 2:
Name:

Name:
• QUESTION 1:

REFLECTION
Group Name ____
1 2
3 4

I’ve 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.
1 2
3 4

Rico Dizon
1 2
3 4

Bianca Roque
I’ve 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.
1 2
3 4

-
1 2
3 4

Factoring Strategies

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