Factoringby

Grouping

Factoring Flow Chart

Is there a GCF ?

2 terms?3 terms ?

4 terms ?

Difference of2 squares ?

Yes

factor

Can you factor by grouping?

No

STOP

How many terms?

Split the Middle

Is “a” = 1 ?

Is a >1?

Use target product target sum

Factor by Grouping

1. Splitting the problem up2. Factor common monomials from

each group using the GCF3. Factor out the common binomial4. Factor the difference of squares

and GCF5. Check

EXAMPLE 10 Factor 3 23 4 12x x x

Factor out GCF

Group Terms

Factor common monomials

Factor out common binomial

Factor the difference of squares

3 23x x

2x

3x

( 3)( 2)( 2)x x x

3 23 4 12x x x none

4 12x

4( 3)x ( 3)x

2 4x

EXAMPLE 11 Factor

22 4 4 8x x x Factor out GCF

Group Terms

Factor common monomials

Factor out common binomial

Factor the difference of squares or check GCF

2

2

2x

2( 2)( 2)x x

2 2 2 2 4x x x

2 2x x 2 4x

2 2x

2

2x

2x

x

EXAMPLE 12 Factor 3 2 2 2x x x Factor GCF

Group Terms

Factor common monomials

Factor out common binomial

Factor the difference of squares or check CGF

3 2x x

2x

1x

none 3 2 2 2.x x x

2 21 xx

2 2x

2 ( 1)x ( 1)x

2 2x

EXAMPLE 13 Factor 3 2 25 25.x x x Factor GCF

Group Terms

Factor common monomials

Factor out common binomial

Factor the difference of squares or check GCF

3 2x x

2x

1x ( 1)( 5)( 5)x x x

none3 2 25 25x x x

25( 1)x ( 1)x

2 25x

25 25x