Name ________________________________________ Date __________________ Class __________________
LESSON
8-3
Using Special Factors to Solve Equations
Practice and Problem Solving: A/B
Factor using the perfect-square technique.
1. x2 + 10xy + 25y2
2. 32x2 + 80xy + 50y2
________________________________________
________________________________________
Factor using the difference of squares technique.
3. 81x2 − 121y2
4. 75x3 − 48x
________________________________________
________________________________________
Solve each equation with special factors.
5. 50x2 = 72
6. 18x3 + 48x2 = − 32x
________________________________________
________________________________________
Solve.
7. A projectile is launched from a hole in the ground one foot deep. Its
height follows the equation h = −16t2 + 8t −1. Use factoring by perfectsquares to find the time when the projectile lands back on the ground.
(Hint: Landing on the ground means projectile height is zero.)
_________________________________________________________________________________________
8. Which of the following are solutions to 4x3 − 16x = 0?
A −2
B −1
C0
D1
E2
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118
13. x = −3,
14. x = −
15. a. −16t2 + 1600 = 0
2
3
b. t = −10, 10
3
,2
2
c. 10 s
Reading Strategies
15. x = 0, −3
1. 1 i 3
2 5
16. x = ,
3 3
17. x =
2. 1 i 12; 2 i 6; 3 i 4
3. minus, minus
1 49
,
2 2
4. (x−)(x−)
5. Possible answer:
(↓ x − ↓) (↓ x − ↓) 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
18. x = −5, 1
19. x =
1 1
,
8 3
20. x = −
1
,1
3
3 −4
3 −3
3 −6
3 −2
21. 4 s and 6 s
Practice and Problem Solving:
Modified
−4
−2
−6
1
− 3 + − 4 i 1 = −13 No
− 4 + − 3 i 1 = −15 No
− 2 + − 6 i 1 = −12 No
− 6 + − 2 i 1 = −20 Yes
1. rectangle
2. Use FOIL to multiply and check your
answer.
2
,2
3
LESSON 8-3
1
5
Practice and Problem Solving: A/B
5. x = −6, 2
1. (x + 5y)2
6. x = −4, 4
7. x = 2,
1
1
3i
3i
3i
3i
Success for English Learners
2. 4; 5; x + 5; x − 1; x + 5; x − 1; −5, 1
4. x = −2, −
−3
6. (3x − 2)(x − 6)
1
1. x = , 2
2
3. x =
1
2. 2(4x + 5y)2
7
2
3. (9x + 11y)(9x − 11y)
4. 3x(5x + 4)(5x − 4)
9
8. x = − , 4
7
5. x =
9. x = −3, 3
6
6
;x= −
5
5
5
10. x = − , 3
2
6. x = 0; x = −
5
11. x =
2
7. t =
4
3
1
s
4
8. A, C, E
12. x = 2
Practice and Problem Solving: C
2
13. x = −3,
3
1. 3(3x + 4y)2
2. x(5x − 6y)2
3
14. x = − , 2
2
3. (x + 3)(x − 3)(x2 + 9)
4. 4x2(3x + 2y)(3x − 2y)
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
500