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1. Lesson 10.4B : Factoring out GCMF
Factor Completely – to express as the product
of prime factors
Ex. Factor completely : 24

6 4
2 32 2
2  2  2  3
Factor the following completely:
1) 5x
2
2) 14x
2
y
3

2. GCF of 12 and 18GCF = 6
GCMF : Greatest Common Monomial Factor – The
greatest monomial that is a factor (will divide EVENLY
into) of all the given monomials.
GCF of 12x
4
y
3
and 18xy
5
GCF = 6xy
3

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 12x
2
and 18x
GCF of coefficients = 6
Common variable(s) : only have one x in common
GCMF = 6x
Find GCMF of 21x
2
and 35x
5
GCF of Coefficients = 7
Common variable factors : two x’s
GCMF = 7x
2

5. Find GCMF of 24x
2
y
3
and 36x
3
y
GCF of coefficients = 12
Common variable factors : two x’s and one y
GCMF = 12x
2
y
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)
12 + 18
Factor : 12 + 18
6 (2 + 3)
2) Use Distributive Property to simplify: 3(x + 7)
3x + 21
Factor: 3x + 21
3(x + 7)
3) Factor: 12x
2
y – 14xy
3

2xy(6x – 7y
2
)

7. 3x(x) + 3x(5)
3x
2
+ 15x
Ex.Distribute 3x(x + 5) Means to multiply the 3x
through the (x + 5)
Ex. Factor 3x
2
+ 15x Means to Divide the GCMF
out of the polynomial (divide
each term by GCMF)
GCMF = 3x Recall how to divide by monomial
x
xx
3
153
2

x
x
x
xx






3
53
3
3
Divide (3x
2
+ 15x) by GCMF (3x)
Factored form is 3x(x + 5)
x
x
x
x
3
15
3
3
2
 5x

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

9. Example: Factor
1)15x
2
– 9
Step 1) GCMF = 3
Step 2) Divide 15x
2
– 9 by the GCMF
35
3
9
3
15
3
915
2
22


x
xx
Step 3) Write as a product of GCMF and result of step 2
3(5x
2
– 3)

10. Factor
1)28a
3
-12a
2

GCMF = 4a
2
Factored Form
4a
2
(7a – 3)
2) 15a – 25b + 20
GCMF = 5
Factored Form
5(3a-5b+4)
3) 16x
5
– 14x
3
+ 26x
2
GCMF = 2x
2
Factored Form
2x
2
(8x
3
– 7x + 13)

11. Homework : Worksheet