**Factoring By Grouping: The Introduction to 4-Terms**

**Method #2**

Factor by Grouping

Factor by Grouping

Recall: Method #1 was factoring the Greatest Common Factor (if one existed)

Steps for Grouping:

1.

Group/Arrange

the Polynomial in "Pairs" With Common Factors

(usually just as it is given)

2. Find the GCF of EACH GROUP

(view each group as a unique problem when finding a gcf now)

3. Factor the GCF from Each Group

5x²

(3x - 2)

When To Use the Grouping Method:

When There Are

4

Terms

When There is NO GCF Common to ALL 4 Terms But a GCF Can Be Found In "

Pairs

" of Terms.

15x³ -10x² +6x - 4

Notice how this polynomial does not have a GCF common to ALL 4 terms?

However, notice that if we look at the terms 2 at a time, we can find sets with common factors.

(

15x³ -10x²

)

GCF:

5x²

(

6x - 4

)

GCF:

2

15x³ -10x² +6x - 4

(

15x³ -10x²

)

+

(

6x - 4

)

2

(3x - 2)

Notice these two factors are the same???

4. Factor Out the Common Binomial Factor

5x² (3x - 2) + 2(3x - 2)

**The

(3x - 2)

is the "common binomial" now. It can be factored out.

5x² (3x - 2) + 2(3x - 2)

(3x - 2)(5x² + 2)

(5x² + 2) is the remaining factor once (3x - 2) is factored out)

(6x - 4)

gcf:

2

(15x³ - 10x²)

gcf:

5x²

Write the Product of the Two Binomial Factors

5.

The Product of the Two Binomial Factors is Your Factored Form

(3x - 2)(5x² + 2)

Summarize

:

**4 Terms???

***No Common GCF???

*******

No Worries!!

1. Make 2 Pairs (

Group

)

2. Factor the GCF From Each Pair

3. Factor Out the Common Binomial (

You should have a match

)

4. Write the Product of 2 Remaining Binomials