Name ________________________________________ Date __________________ Class__________________
Review for Mastery
LESSON
8-4
Factoring ax2 + bx + c
When factoring ax2 + 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 2x2 + 11x + 15. Check your
answer.
2x2 + 11x + 15 = (
x+
x+
)(
Factor 3x2 − 23x + 14. Check your answer.
3x2 − 23x + 14 = (
)
x+
)(
x+
)
Factors
of 2
Factors
of 15
Outer + Inner
1 and 2
1 and 15
1 • 15 + 2 • 1 = 17 8
1 and 3 −1 and −14 1 • (−14) + 3 • (−1) = −17 8
1 and 2
15 and 1
1 • 1 + 2 • 15 = 31 8
1 and 3 −14 and −1 1 • (−1) + 3 • (−14) = −42 8
1 and 2
5 and 3
1 • 3 + 2 • 5 = 13 8
1 and 3 −2 and −7
1 • (−7) + 3 • (−2) = −13 8
1 and 2
3 and 5
1 • 5 + 2 • 3 = 11 9
1 and 3 −7 and −2
1 • (−2) + 3 • (−7) = −23 9
Factors
of 3
(x + 3) (2x + 5)
Factors
of 14
Outer + Inner
(x − 7) (3x − 2)
Check:
Check:
2
(x − 7) (3x − 2) = 3x2 − 2x − 21x + 14
(x + 3) (2x + 5) = 2x + 5x + 6x + 15
= 2x2 + 11x + 15 9
= 3x2 + 23x + 14 9
1. Factor 5x2 + 12x + 4 by filling in the blanks below.
Outer + Inner
Factors
Factors
and
and
•
+
•
=
and
and
•
+
•
=
and
and
•
+
•
=
_____________________________________
Factor each trinomial.
2. 3x2 + 7x + 4
________________________
3. 2x2 − 13x + 21
_________________________
4. 4x2 + 8x + 3
________________________
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8-30
Holt McDougal Algebra 1
Name ________________________________________ Date __________________ Class__________________
LESSON
8-4
Review for Mastery
Factoring ax2 + 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 2x2 + 7x − 15. Check your answer.
2x2 + 7x − 15 = (
x+
)(
x+
)
Factors of 2
Factors of −15 Outer + Inner
1 and 2
−3 and 5
1 • 5 + 2 • (−3) = −1 8
1 and 2
3 and −5
1 • (−5) + 2 • 3 = 1 8
1 and 2
−5 and 3
1 • 3 + 2 • (−5) = −7 8
1 and 2
5 and −3
1 • (−3) + 2 • 5 = 7 9
Check:
(x + 5) (2x − 3) = 2x2 − 3x + 10x − 15
(x + 5) (2x − 3)
= 2x2 + 7x − 15
When a is negative, factor out −1. Then factor as shown previously.
Factor −5x2 + 28x + 12. Check your answer.
−5x2 + 28x + 12
−1(5x2 − 28x − 12) = −1(
x+
)(
x+
)
Factors of 5
Factors of −12 Outer + Inner
1 and 5
−2 and 6
1 • 6 + 5 • (−2) = −4 8
1 and 5
2 and −6
1 • (−6) + 5 • 2 = 4 8
1 and 5
6 and −2
1 • (−2) + 5 • 6 = 28 8
1 and 5
−6 and 2
1 • 2 + 5 • (−6) = −28 9
Check:
−1(x − 6) (5x + 2)
−1(x − 6) (5x + 2)
= −1(5x2 + 2x − 30x − 12)
= −1(5x2 − 28x − 12)
= −5x2 + 28x + 12
Factor each trinomial.
5. 3x2 − 7x − 20
________________________
6. 5x2 + 34x − 7
_________________________
7. −2x2 + 3x + 5
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
8-31
Holt McDougal Algebra 1
12. −1(2x + 9)(2x − 5)
Reading Strategies
13. (3x + 50)(2x − 3)
14. (4x + 5)(x + 2)
15. (3k − 4)(3k − 2)
16. (8n + 11)(3n − 2)
1. 1 i 3
17. (7x + 4)(3x − 4)
18. (6p + 7)(3p − 2)
2. 1 i 12; 2 i 6; 3 i 4
19. −1(13w − 25)(w − 1)
3. minus, minus
20. (12x + 5)(x + 6)
4. (
21. (3y + 1)(4y − 15)
5. Possible answer:
22. 4x + 5
x−
x−
)(
( x− )( x− )
23. 2x − 9 inches
Review for Mastery
1.
Outer + Inner
Factors
Factors
1; 5
1; 4
1; 4; 5; 1; 9
1; 5
4; 1
1; 1; 5; 4; 21
1; 5
2; 2
1; 2; 5; 2; 12
)
Outer + Inner
3
−1 1
−12 3 i −12 + −1 i 1 = −37 No
3
−12 1
−1 3 i −1 + −12 i 1 = −15 No
3
−4 1
−3 3 i −3 + −4 i 1 = −13 No
3
−3 1
−4 3 i −4 + −3 i 1 = −15 No
3
−6 1
−2 3 i −2 + −6 i 1 = −12 No
3
−2 1
−6 3 i −6 + −2 i 1 = −20 Yes
6. (3x − 2)(x − 6)
(x + 2)(5x + 2)
2. (3x + 4)(x + 1)
LESSON 8–5
3. (2x − 7)(x − 3)
4. (2x + 3)(2x + 1)
5. (3x + 5)(x − 4)
6. (5x − 1)(x + 7)
Practice A
1. 5; x; 5
7. −1(2x − 5)(x + 1)
2. 1; 3x; 3x; 1; 3x; 2; 1
Challenge
1. 4 −7 −15
12 15
4 5 0
2. 3
3. (6x + 1)
4. (8x − 5)
3. (x − 9)2
4 −32
−12 32
3 −8 0
4. (6x + 2)2
5. 6 is not a perfect square
6. 12x ≠ 2(2x i 6).
7. a. x + 4 in.
b. 4(x + 4) in.
c. 48 in.
5. (x − 1)(x + 3)(x + 5)
6. (x + 4)(2x − 1)(x − 5)
8. 3; 3
Problem Solving
3
9. 2p; 7; 2p; 7
3
10. (t + 12)(t − 12)
11. (4x5 + y)(4x5 − y)
1. (x + 3) cm
12. 20 is not a perfect square.
2. −1(4t − 4)(4t + 1)
or −4(4t + 1)(t − 1); 0 feet
13. the operation between the two squares
is addition.
3. (3x + 3) ft; increase of 2 ft
Practice B
4. length increased by 5 ft,
width increased by 7 ft
1. yes; (x + 3)2
2. yes; (2x + 5)2
4. yes; (3x − 2)2
5. C
6. F
3. no; 24x ≠ 2(6x i 4)
7. B
8. G
5. 4(2x + 3) ft; 28 ft
6. yes; (x + 4)(x − 4)
7. no; 200 is not a perfect square.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A17
Holt McDougal Algebra 1