Name_____________________________________ Class____________________________ Date ________________
Lesson 9-8
Factoring by Grouping
Lesson Objectives
1 Factor polynomials with four terms
2 Factor trinomials by grouping
NAEP 2005 Strand: Algebra
Topic: Variables, Expressions, and Operations
Local Standards: ____________________________________
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Vocabulary and Key Concepts.
Factoring Polynomials
1. Factor out the greatest common factor (GCF).
2. If the polynomial has two terms or three terms, look for a difference
of two squares, a product of two squares, or a pair of binomial factors.
3. If there are four or more terms, group terms and factor to find
common binomial factors.
4. As a final check, make sure there are no common factors other than 1.
Factor by grouping is
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Examples.
1 Factoring a Four-Term Polynomial Factor 6x3 3x2 4x 2.
(
6x3 3x2 4x 2 Check
(
Factor the GCF from each group of
two terms.
)
(2x 1) 2
)(3x2 2)
6x3 3x2 4x 2 0
(
Factor out
(
).
)(3x2 2)
6x3 2
Use FOIL.
6x3 3x2 4x 2 ✔
Write in standard form.
2 Factoring Completely Factor 8t 4 12t 3 16t 24.
(2
8t 4 12t 3 16t 24 [
3t 3 (2t 4(2t 3)(
4
Daily Notetaking Guide
) 2(
2)
6
)
Factor out the GCF,
)]
3
.
Factor by grouping.
Factor again.
Algebra 1 Lesson 9-8
173
Name_____________________________________ Class____________________________ Date________________
3 Finding the Dimensions of a Rectangular Prism A rectangular prism has
a volume of 36x3 51x2 18x. Factor to find the possible expressions for
the length, width, and height of the prism.
Factor 36x3 51x2 18x.
(12x2 6)
Step 2
12 6 Step 3
Factors
S
4
S 4
12
Step 5
(
3x[
3x(
.
Find the product ac.
Sum
Find two factors of ac that have sum b.
12 S
8
Step 4
Factor out the GCF,
8
S
3x 12x2 9x (3x 2) )(
3 3x Use mental math to determine a good place to start.
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Step 1
)
Rewrite the trinomial.
(3x 2)]
)
The possible dimensions of the prism are
Factor by grouping.
Factor again.
,
, and
.
Quick Check.
a. 5t4 20t 3 6t 24
b. 2w3 w2 14w 7
2. 45m4 9m3 30m2 6m
3. Find expressions for the possible dimensions of each rectangular prism.
a.
b.
6g3 20g2 16g
174
Algebra 1 Lesson 9-8
3m3 10m2 3m
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. Factor each expression. Check your answer.