Factoring by Grouping

Factoring Technique #3

Factoring By Groupingfor polynomials

with 4 or more terms

Factoring By Grouping1. Group the first set of terms and last

set of terms together with parentheses.2. Factor out the GCF from each group

so that both sets of parentheses contain the same factors.

3. Factor out the GCF again (the GCF is the factor from step 2).

Factor Out the Greatest Common Factor (GCF)

ax + bx = x(a+b)

a(x + 5) + b(x + 5) = (x + 5) (a+b)

BACK

Factor Out the Greatest Common Factor

x(3a + 2) + 7(3a + 2) =(3a + 2)

BACK

7x

Step 1: Group into two groups

3 2

3 4 12b b b Example 1:

b3 3b2 4b 12 Step 2: Factor out GCF from each group b2 b 3 4 b 3 Step 3: Factor out GCF again b 3 b2 4

3xa + 2x + 21a + 14

Factor Out the Common Factor

x(3a + 2) + 7(3a + 2) =

(3a + 2)

This is called factoring by grouping.BACK

7x

Example: Factor 6x2 – 3x – 4x + 2 by grouping

6x2 – 3x – 4x + 2

123 xx

BACK

122 x

2312 xx

Factor xy + 2x + 4y + 8 by grouping

xy + 2x + 4y + 8

2yx

BACK

24 y

42 xy

3 22 16 8 64x x x

2 x3 8x2 4x 32 2 x3 8x2 4x 32 2 x 2 x 8 4 x 8 2 x 8 x2 4 2 x 8 x 2 x 2

Example: