Factoring by Grouping

1
Factoring by Grouping
ALGEBRA 1 LESSON 9-8
(For help, go to Lessons 9-2 and 9-3.)
Find the GCF of the terms of each
polynomial. 1. 6y2 12y 4 2. 9r3 15r2
21r 3. 30h3 25h2 40h 4. 16m3 12m2
36m Find each product. 5. (v 3)(v2
5) 6. (2q2 4)(q 5) 7. (2t 5)(3t 4) 8. (4x
1)(x2 2x 3)
Check Skills Youll Need
9-8
2
Factoring by Grouping
ALGEBRA 1 LESSON 9-8
1. 6y2 12y 4 2. 9r3 15r2 21r 6y2 2
3 y y 9r3 3 3 r r r 12y 2
2 3 y 4 2 2 15r2 3 5 r r 21r
3 7 r GCF 2 GCF 3r 3. 30h3 25h2
40h 4. 16m3 12m2 36m 30h3 2 3 5 h
h h 16m3 2 2 2 2 m m m 25h2
5 5 h h 12m2 2 2 3 m m 40h
2 2 2 5 h 36m 2 2 3 3 m GCF
5h GCF 2 2 m 4m
Solutions
5. (v 3)(v2 5) (v)(v2) (v)(5) (3)(v2)
(3)(5) v3 5v 3v2 15 v3 3v2 5v
15
9-8
3
Factoring by Grouping
ALGEBRA 1 LESSON 9-8
Solutions (continued)
6. (2q2 4)(q 5) (2q2)(q) (2q2)(5)
(4)(q) (4)(5) 2q3 10q2 4q 20
7. (2t 5)(3t 4) (2t)(3t) (2t)(4)
(5)(3t) (5)(4) 6t2 8t 15t 20 6t2
7t 20
8. (4x 1)(x2 2x 3) (4x)(x2) (4x)(2x)
(4x)(3) (1)(x2) (1)(2x) (1)(3) 4x3
8x2 12x x2 2x 3 4x3 (8 1)x2
(12 2)x 3 4x3 7x2 10x 3
9-8
4
Factoring by Grouping
ALGEBRA 1 LESSON 9-8
Factor 6x3 3x2 4x 2.
6x3 3x2 4x 2 3x2(2x 1) 2(2x
1) Factor the GCF from each group of two terms.
(2x 1)(3x2 2) Factor out (2x 1).
Quick Check
9-8
5
Factoring by Grouping
ALGEBRA 1 LESSON 9-8
Factor 2t3 3t2 4t 6.
2t3 3t2 4t 6
t2(2t 3) 2(2t 3) Factor by grouping.
(2t 3)(t2 2) Factor again.
Quick Check
9-8
6
Factoring by Grouping
ALGEBRA 1 LESSON 9-8
Factor each expression. 1. 10p3 25p2 4p
10 2. 36x4 48x3 9x2 12x 3. 16a3 24a2
12a 18
(5p2 2)(2p 5)
3x(4x2 1)(3x 4)
2(4a2 3)(2a 3)
9-8
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Factoring to Solve Quadratic Equations
ALGEBRA 1 Lesson 10-4
Solve (2x 3)(x 4) 0 by using the Zero
Product Property.
(2x 3)(x 4) 0
Quick Check
10-4
8
Factoring to Solve Quadratic Equations
ALGEBRA 1 Lesson 10-4
Solve x2 7x 6x 42 0 by factoring.
x (x 7) 6 (x 7) 0
Factor by grouping.
Quick Check
10-4
9
Factoring to Solve Quadratic Equations
ALGEBRA 1 Lesson 10-4
Solve 3x2 7x 9x 21 by factoring.
Quick Check
10-4