Here are the step-by-step procedures to factor polynomials using the greatest common monomial factor: 1. Find the greatest common factor (GCF) of all the numerical coefficients. 2. Find the greatest common factor (GCF) of all the variables with the least exponents. 3. Multiply the GCF of the numerical coefficients with the GCF of the variables to get the greatest common monomial factor (GCMF). 4. Divide the original polynomial by the GCMF. The quotient is the other factor.

2. Came from word “Poly” which means “Many” and
“Nominal” which means “Terms”
12x3 y5 – 20x5 y2 z

3. -In algebra, factoring is a technique to
simplify an expression by reversing
the multiplication process
-It is a process to get the factors of
polynomials
FACTORING

4. 4 . 4 = 16
factors
Product
Multiplication

5. 4 . 4
16 =
factors
Product
Factoring
8 . 2
16 . 1

6. FACTORING
Sum and Difference of two cubes
Factoring Using Greatest Common Monomial Factors
Difference of Two Squares
Perfect Square Trinomial
General Polynomials

7. Factoring Using Greatest Common Monomial Factors
1. Factor 8x2 + 16x
a.Find the Greatest Common Factor of the
numerical coefficients.
8 =
16 =
2 . 2 . 2
2 . 2 . 2 . 2
GCF = 2 .2 .
= 8
2 .

8. Factoring Using Greatest Common Monomial Factors
Factor 8 x2 – 16 x
b. Find the GCF of variable. It is the variable
with the least exponent that appears in
each term of the polynomial.
GCF = x1
= x

9. Factoring Using Greatest Common Monomial Factors
Factor 8x2 – 16x
c. Find the GCMF of the polynomial by
Multiplying the of the Greatest Common Factor
in (a) and (b).
GCMF = 8 . x
= 8x

10. Factoring Using Common Monomial Factors
Factor 8x2 – 16x
d. To completely factor the given polynomial, divide the
polynomial by its GCMF, the resulting quotient is the other
factor. 8x2 – 16x
8x
1x2-1
– 2x1-1
1x1 - 2
8x
or x - 2

11. Factoring Using Common Monomial Factors
Factor 8x2 – 16x
8x (x - 2)

12. Factoring Using Greatest Common Monomial Factors
1. Factor 12x3 y5 – 20x5 y2 z
a.Find the Greatest Common Factor of the
numerical coefficients.
12 =
20 =
2 . 2 . 3
2 . 2 . 5
GCF = 2 . 2
= 4

13. Factoring Using Greatest Common Monomial Factors
Factor 12 x3 y5 – 20 x5 y2 z
b. Find the GCF of variable. It is the variable
with the least exponent that appears in
each term of the polynomial.
GCF = x y
3 2

14. Factoring Using Greatest Common Monomial Factors
Factor 12x3 y5 – 20x5 y2 z
c. Find the GCMF of the polynomial by
Multiplying the of the Greatest Common Factor
in (a) and (b).
GCMF = 4 . x3 y2
= 4x3 y2

15. Factoring Using Common Monomial Factors
Factor 12x3 y5 – 20x5 y2 z
d. To completely factor the given polynomial, divide the
polynomial by its GCMF, the resulting quotient is the other
factor. 12x3 y5 – 20x5 y2 z
4x3 y2 4x3 y2
3x3-3 y5-2 – 5 x5-3 y2-2 z
3y3 – 5x2z

16. Factoring Using Common Monomial Factors
Factor 12x3 y5 – 20x5 y2 z
4x3 y2 (3y3 – 5x2z)

17. Factoring Using Greatest Common Monomial Factors
1. Factor 12x5 y4 – 16x3 y4 + 28x6
a.Find the Greatest Common Factor of the
numerical coefficients.
12 =
16 =
2 . 2 . 3
2 . 2 . 7
GCF = 2 . 2
= 4
28 =
2 . 2 . 2 . 2

18. Factoring Using Greatest Common Monomial Factors
Factor 12x5 y4 – 16x3 y4 + 28x6
b. Find the GCF of variable. It is the variable
with the least exponent that appears in
each term of the polynomial.
GCF = x3

19. Factoring Using Greatest Common Monomial Factors
1. Factor 12x5 y4 – 16x3 y4 + 28x6
c. Find the GCMF of the polynomial by
Multiplying the of the Greatest Common Factor
in (a) and (b).
GCMF = 4 . x3
= 4x3

20. Factoring Using Common Monomial Factors
Factor 12x5 y4 – 16x3 y4 + 28x6
d. To completely factor the given polynomial, divide the
polynomial by its GCMF, the resulting quotient is the other
factor.
4x3 4x3
3 x5-3 y4
– + x6-3
3x2 y4 – 4y4 + 7x3
12x5 y4 – 16x3 y4 + 28x6
4x3
4X3-3 7
y4

21. Factoring Using Common Monomial Factors
Factor 12x5 y4 – 16x3 y4 + 28x6
4x3 (3x2 y4 – 4y4 + 7x3 )

22. What are the procedures in
factoring polynomials using
the Greatest Common
Monomial Factor?

23. Find the factors of the following polynomials
1. 36ab + 6b
2. 34x2 – 51xy + 17x
3. 5x4y3 – 10x3y4 + 15x2y5
4. 3x (x- y) – 6y ( x- y )
5. 4x5 – 2x4 + 8x3