Factoring Day 1

GCFDifference of 2 Squares

factor by grouping

GCFFind the Greatest Common Factor

Example 125 15a

Example 2

23 9n n

Example 33 26 10k k

Example 436 18a ab

Example 5

2 2 33 15a b ab

GCF

Find the Greatest Common Factor

Example 1 25 15a

5 2 3a

GCF

Find the Greatest Common Factor

Example 2 23 9n n

3n 3n

GCF

Find the Greatest Common Factor

Example 3 3 26 10k k22k 3 5k

GCF

Find the Greatest Common Factor

Example 4 36 18a ab

6a 2 3a b

GCF

Find the Greatest Common Factor

Example 5 2 2 33 15a b ab23ab 5a b

Difference of 2 Squares

2. Are there only 2 terms?

3. Is it a difference? (subtraction)

4. Are they both perfect squares?

1.Is there a GCF?

Perfect Squares

6x

4x

10x

2x

8x

1

4 64

9 81

16 100

25 121

36 144

49

Difference of 2 Squares

2 9x 1. Is there a GCF?

2. Are there only 2 terms?

3. Is it a difference? (subtraction)

4. Are they both perfect squares?

( 3)x ( 3)x 2 3 3 9x x x

2 9x

Example 6

Factor 22 8x 22( 4)x

2( 2)( 2)x x

Example 7

Factor 29 1x (3 1)x (3 1)x

Example 8

Factor 4 16x 2( 4)x 2( 4)x

2( 4)x ( 2)x ( 2)x

Example 9

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

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

11Factor

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 12Factor 3 2 2 2x x x Factor GCF Group TermsFactor common monomialsFactor out common binomialFactor 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 TermsFactor common monomialsFactor out common binomialFactor 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