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Factoring By Grouping: The Introduction to 4-Terms

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Beth Dodson

on 24 January 2017

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Transcript of Factoring By Grouping: The Introduction to 4-Terms

Factoring By Grouping: The Introduction to 4-Terms
Method #2
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
Full transcript