1. Lesson 10.4B : Factoring out GCMF
Factor Completely – to express as the product of prime factors
Ex. Factor completely : 24
6 4
2  2  2  3
2 3
2 2
Factor the following completely:
1) 5x2 2) 14x2y3

2. GCF = 6
GCF of 12 and 18
GCF of 12x4y3 and 18xy5
GCF = 6xy3
GCMF : Greatest Common Monomial Factor – The greatest monomial that is a factor (will divide EVENLY into) of all the given monomials.

3. To find the GCMF of two or more Monomials
First find the GCF of the coefficients
Find the largest power of each variable that is COMMON to all the monomials
The GCMF = product of GCF of coefficients and common variable factors

4. Ex. Find GCMF of 12x2 and 18x
GCF of coefficients = 6
Common variable(s) : only have one x in common
GCMF = 6x
Find GCMF of 21x2 and 35x5
GCF of Coefficients = 7
Common variable factors : two x’s
GCMF = 7x2

5. Find GCMF of 24x2y3 and 36x3y
GCF of coefficients = 12
Common variable factors : two x’s and one y
GCMF = 12x2y
NOW, we are going to use GCMF’s to Factor Quadratic Expressions. Factoring Out the GCMF is the inverse (un-doing) of the Distributive Property

6. To factor – undoing distributive property
1) Perform Distributive Property: 6(2 + 3)
Factor :
6 (2 + 3)
2) Use Distributive Property to simplify: 3(x + 7)
3x + 21
Factor: 3x + 21
3(x + 7)
3) Factor: 12x2y – 14xy3
2xy(6x – 7y2)

7. Ex.Distribute 3x(x + 5) Means to multiply the 3x through the (x + 5)
3x(x) + 3x(5)
3x2 + 15x
Ex. Factor 3x2 + 15x Means to Divide the GCMF out of the polynomial (divide each term by GCMF)
GCMF = 3x Recall how to divide by monomial
Divide (3x2 + 15x) by GCMF (3x)
Factored form is 3x(x + 5)

8. To factor a polynomial by factoring out the GCMF:
Find the GCMF
Divide the polynomial (each term of the polynomial) by the GCMF
Write the polynomial as the product of the GCMF and the result from step #2

9. Step 2) Divide 15x2 – 9 by the GCMF
Example: Factor
15x2 – 9
Step 1) GCMF = 3
Step 2) Divide 15x2 – 9 by the GCMF
Step 3) Write as a product of GCMF and result of step 2
3(5x2 – 3)

10. Factor
28a3-12a2
GCMF = 4a2
2) 15a – 25b + 20
GCMF = 5
Factored Form
5(3a-5b+4)
Factored Form 4a2(7a – 3)
3) 16x5 – 14x3 + 26x2
GCMF = 2x2
Factored Form
2x2(8x3 – 7x + 13)

11. Homework : Worksheet