Factoring Using the Distributive Property

GCF and Factor by Grouping

1) Factor GCF of 12a2 + 16a

12a2 = 16a =

2 2 3 a a

2 2 2 2

2 2 a = 4a212 16a a 4a (3 )a 4a (4)

Use distributive

property

4a (3 4)a

a

Using GCF and Grouping to Factor a Polynomial

First, use parentheses to group terms with common factors.

Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s.

and bring down one of the other ( ) since they’re both the same.

2) Factor 4 8 3 6ab b a ( ) ( )4b ( 2)a 3 ( 2)a

(4 3)b ( 2)a

Using GCF and Grouping to Factor a Polynomial

First, use parentheses to group terms with common factors.

Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s.

and bring down one of the other ( ) since they’re both the same.

23) Factor 6 15 8 20x x x ( ) ( )3x (2 5)x 4 (2 5)x

(3 4)x (2 5)x

Using GCF and Grouping to Factor a Polynomial

First, use parentheses to group terms with common factors.Next, factor the GCF from each grouping.Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same.

24) Factor 2 6 3 9a a a ( ) ( )2a ( 3)a 3 ( 3)a

(2 3)a ( 3)a

Using the Additive Inverse Property to Factor Polynomials.

When factor by grouping, it is often helpful to be able to recognize binomials that are additive inverses. 7 – y is

y – 7 By rewriting 7 – y as -1(y – 7)

8 – x is x – 8 By rewriting 8 – x as -1(x – 8)

5) Factor 35 5 3 21x xy y ( )( )5x (7 )y 3 ( 7)y

( 5 3)x ( 7)y

Factor using the Additive Inverse Property.

5x( 1) ( 7)y 3 ( 7)y

5x ( 7)y 3 ( 7)y

6) Factor 2 8 4c cd d ( ) ( )c (1 2 )d 4 (2 1)d

( 4)c (2 1)d

Factor using the Additive Inverse Property.

c ( 1) (2 1)d 4 (2 1)d

c (2 1)d 4 (2 1)d

27) Factor 10 14 15 21x xy x y

There needs to be a + here so change the minus to a

+(-15x)

210 14 ( 15 ) 21x xy x y •Now group your common terms.•Factor out each sets GCF.•Since the first term is negative, factor out a negative number.•Now, fix your double sign and put your answer together.

( ) ( )2x(5 7 )x y 3( ) (5 7 )x y

(2 3)x (5 7 )x y

8) Factor 8 6 12 9ax x a

There needs to be a + here so change the minus to a

+(-12a)

8 6 ( 12 ) 9ax x a •Now group your common terms.•Factor out each sets GCF.•Since the first term is negative, factor out a negative number.•Now, fix your double sign and put your answer together.

( ) ( )2x (4 3)a 3( ) (4 3)a

(2 3)x (4 3)a

Summary

A polynomial can be factored by grouping if ALL of the following situations exist. There are four or more terms. Terms with common factors can be

grouped together. The two common binomial factors

are identical or are additive inverses of each other.