• Recall: By the distributive property, we havex ( x + 2 ) = x² + 2x

• Now we’re given a polynomial expression and we want to perform the “opposite” of the distributive property which we call “factoring”.

• Factoring means writing a sum or difference as a product.

Factoring out the GCF(Greatest Common Factor)

2

2

5 4 3

9 6 7 5 4 4 3 3

1) 2 6

2) 35 25

3) 12 15 27

4) 30 18 12 36

x x

a a

x x x

x y x y x y x y

Examples

Factor each of the polynomials

1) ( 5) 3( 5)

2) 3 ( 9) ( 9)

3) 4( 5) ( 5)

b b b

z z z

x x x

Examples

1. Group terms.

2. Factor GCF out of each grouped binomial.

3. Now factor out GCF (a binomial) from the two factors found in step two.

3 2

3 2

3 2

3 2

1) 3 4 12

2) 6 3 2 1

3) 7 5 7 5

4) 3 10

x x x

x x x

x x x

x x x

Factoring by grouping

Factor each of the polynomials completely

22334

2

2233)2

55)1

cbcbcbb

yxyxy

Examples