Name
Date
Class
Reteach
LESSON
Factoring ax 2 ⫹ bx ⫹ c
8-4
When factoring ax 2 bx c, first find factors of a and c. Then check the products
of the inner and outer terms to see if the sum is b.
Factor 2x 2 ⫹ 11x ⫹ 15. Check your
answer.
2x 2 11x 15 x
Factor 3x 2 ⫺ 23x ⫹ 14. Check your
answer.
x
Factors
of 2
Factors
of 15
Outer Inner
1 and 2
1 and 2
1 and 2
1 and 2
1 and 15
15 and 1
5 and 3
3 and 5
1 15 2 1 17 7
1 1 2 15 31 7
1 3 2 5 13 7
1 5 2 3 11 3
3x 2 23x 14 Factors
of 3
x
x
Outer Inner
Factors
of 14
1 and 3 1 and 14 1 14 3 1 17 7
1 and 3 14 and 1 1 1 3 14 42 7
1 and 3 2 and 7 1 7 3 2 13 7
1 and 3 7 and 2
1 2 3 7 23 3
x 7 3x 2 x 3 2x 5 Check:
Check:
x 7 3x 2 3x 2 2x 21x 14
x 3 2x 5 2x 2 5x 6x 15
2
3x 23x 14 3
2
2x 11x 15 3
1. Factor 5x 2 12x 4 by filling in the blanks below.
Factors
Outer Inner
Factors
1
and
5
1
and
4
1
4
5
1
9
1
and
5
4
and
1
1
1
5
4
21
1
and
5
2
and
2
1
2
5
2
12
x
⫹ 2 5x ⫹ 2 Factor each trinomial.
2
2. 3x 7x 4
3x
3. 2x 2 13x 21
⫹ 4 x ⫹ 1 Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c08-4_rt.indd 30
2x
⫺ 7 x ⫺ 3 30
4. 4x 2 8x 3
2x
⫹ 3 2x ⫹ 1 Holt Algebra 1
12/26/05 8:13:45 AM
Process Black
Name
LESSON
8-4
Date
Class
Reteach
Factoring ax 2 ⫹ bx ⫹ c (continued)
When c is negative, one factor of c is positive and one is negative. You can stop checking
factors when you find the factors that work.
Factor 2x 2 ⫹ 7x ⫺ 15. Check your answer.
2x 2 7x 15 Factors of 2
1 and 2
1 and 2
1 and 2
1 and 2
x
x
Factors of 15 Outer Inner
3 and 5
1 5 2 3 3 and 5
1 5 2 3
5 and 3
1 3 2 5 5 and 3
1 3 2 5
1 7
17
7 7
73
Check:
x 5 2x 3 x 5 2x 3 2x 2 3x 10x 15
2
2x 7x 15
When a is negative, factor out 1. Then factor as shown previously.
Factor ⫺5x 2 ⫹ 28x ⫹ 12. Check your answer.
5x 2 28x 12
1 5x 2 28x 12 1 Factors of 5
1 and 5
1 and 5
1 and 5
1 and 5
x
x
Factors of 12 Outer Inner
2 and 6
1 6 5 2 2 and 6
1 6 5 2
6 and 2
1 2 5 6
6 and 2
1 2 5 6 4 7
47
28 7
28 3
Check:
1 x 6 5x 2 1 x 6 5x 2 2
1 5x 2x 30x 12 2
1 5x 28x 12 2
5x 28x 12
Factor each trinomial.
2
5. 3x 7x 20
3x
⫹ 5 x ⫺ 4 Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c08-4_rt.indd 31
6. 5x 2 34x 7
5x
⫺ 1 x ⫹ 7 31
7. 2x 2 3x 5
⫺1 2x ⫺ 5 x ⫹ 1 Holt Algebra 1
12/26/05 8:13:46 AM
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Holt Algebra 1
12/28/05 8:02:01 PM