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1. Grade 8 – Mathematics
Quarter I
FACTORING POLYNOMIALS

2. Objectives:
• find the greatest common factor (GCF)
by listing or prime factorization;
• factor polynomials completely with
common monomial factor; and
• use distributive property to factor
polynomials.

3. • Greatest Common Factor (GCF)
• Standard Form
• Polynomial
• Monomial
• Prime factors

4. Greatest Common Factor (GCF)
GCF: 3𝑥2
6𝑥2
: (2)∙(3)∙(𝑥2
)
15𝑥4
: (3)∙(5)∙(𝑥4
)
GCF: 3𝑥2
6: 1, 2, 3, 6, 𝑥2
15: 1, 3, 5, 15, 𝑥4
- refers to the common factor having the
greatest numerical factor and with
variables having the least degree.
Example: 6𝑥2
and 15𝑥4

5. Find the GCF of each pair of monomials.
1. 6a and 18ab
= (2)∙(3)∙(a)
6a: (2)∙(3)∙(a)
18ab: (2)∙(3)∙(3)∙(a)∙(b)
GCF is 6a
2. 10a and 12𝑎2
b
= (2)∙(a)
10a: (2)∙(5)∙(a)
12𝑎2
b: (2)∙(2)∙(3)∙(𝑎2
)∙(b)
GCF is 2a

6. Find the GCF of each pair of monomials.
3. −8𝑥2
y and 16xy
= (2)∙(2)∙(2)∙(x)∙(y)
−8𝑥2
y: -(2)∙(2)∙(2)∙(𝑥2
)∙(y)
16xy: (2)∙(2)∙(2)∙(2)∙(x)∙(y)
GCF is 8xy
4. 8𝑎𝑏3
and 10𝑎2
𝑏2
= (2)∙(a)∙(𝑏2
)
GCF is 2a𝑏2
8𝑎𝑏3:(2)∙(2)∙(2)∙(a)∙(𝑏3)
10𝑎2
𝑏2
:(2)∙(5)∙(𝑎2
)∙(𝑏2
)

7. FACTORING POLYNOMIAL
POLYNOMIAL
- rewriting a polynomial as a product of
polynomials of smaller degree.
GCF FACTORED FORM
4𝑥2
+ 6x
3𝑥2
+ 6x
6𝑥4
- 14𝑥2
2x
3x
2𝑥2
2x(2x + 3)
3x(x + 2)
2𝑥2
(3𝑥2
- 7)

8. 4𝑥2
+ 6x = 2x(2x) + 2x(3) Use GCF to rewrite the
polynomial
= 2x(2x + 3) Use the distributive property
3𝑥2
+ 6x = 3x(x) + 3x(2)
= 3x(x + 2)
Use GCF to rewrite the
polynomial
Use the distributive property

9. 6𝑥4
- 14𝑥2
= 2𝑥2
(3𝑥2
) - 2𝑥2
(7)
= 2𝑥2
(3𝑥2
- 7)
7a(a+3) - c(a+3)
(a + 3)(7a – c)
8m(n+3) + p(n+3)
(n + 3)(8m + p)

10. 4(3b-1) + 5a(1-3b) + 4c(3b-1)
4(3b-1) - 5a(-1+3b) + 4c(3b-1)
4(3b-1) - 5a(3b-1) + 4c(3b-1)
(3b-1)(4 - 5a + 4c)