Name ________________________________________ Date __________________ Class __________________
LESSON
8-2
Solving Equations by Factoring ax2 + bx + c
Practice and Problem Solving: A/B
Solve the equations by factoring.
1. 2x2 − 3x = 2x − 2
2. 3x2 − 4x = 6x − 3
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3. 3x2 − 7x = x − 4
4. 5x2 + 6x = −5x − 2
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5. 4x2 + 16x − 48 = 0
6. 2x2 − 32 = 0
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7. 2x2 − 7 = 14 − 11x
8. 7x2 − 12x = 36 + 7x
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9. 5x2 = 45
10. 2x2 − 7x = 15 − 6x
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11. 4x2 − 20x = −25
12. 5x2 − 20x + 20 = 0
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13. 3x2 + 5x = 6 − 2x
14. 2x2 + 3x + 6 = 4x
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15. 3x2 = 9x
16. 9x2 − 13x = 8x − 10
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17. 4x2 − 50x + 49 = 50x
18. 4x2 + 21x = 6x − 14
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19. 24x2 − x = 10x − 1
20. 3x2 + 12x − 15 = 0
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Solve.
21. The height of a flare fired from the deck of a ship in distress can be
modeled by h = −16t 2 + 104t + 56, where h is the height in feet of the
flare above water and t is the time in seconds. Find the time it takes
the flare to hit the water.
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
113
Reading Strategies
10. x = −
1. Both the product and sum are positive, so
the factors are both positive.
11. x =
2. Both the sum and product are negative,
so one factor is positive and the other is
negative.
5
,3
2
5
2
12. x = 2
2
3
3. The sum is negative and the product is
positive, so both factors are negative.
13. x = −3,
4. (x + 5)(x + 6)
14. no solution
5. (x − 7)(x + 4)
15. x = 0, 3
6. (x + 6)(x − 4)
16. x =
2 5
,
3 3
17. x =
1 49
,
2 2
7. (x + 9)(x − 8)
8. (x + 3)(x + 12)
9. (x − 7)(x − 7)
10. (x − 3)(x + 8); x = 3, (x = −8)
18. x = −
11. (x + 4)(x + 11); x = −4, x = − 11
7
, −2
4
1 1
,
8 3
12. (x − 6)(x − 7); x = 6, x = 7
19. x =
Success for English Learners
20. x = −5, 1
1. positive; negative
21. 7 s
2. positive; negative
Practice and Problem Solving: C
3. negative
4. sum; product
LESSON 8-2
Practice and Problem Solving: A/B
1. x =
1
,2
2
2. x =
1
,3
3
2
,2
3
1. x =
1
,2
2
3. x =
2. x =
1
,3
3
4. x = −2, −
3. x =
2
,2
3
5. x = 2 or −6
4. x = −2, −
6. x = −4, 4
1
5
7. x = −7,
5. x = −6, 2
8. x = −
6. x = −4, 4
7. x = −7,
8. x = −
1
5
3
2
9
,4
7
9. x = −3, 3
3
2
10. x = −
9
,4
7
11. x =
9. x = −3, 3
5
,3
2
5
2
12. x = 2
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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