Download Practice 5-4 - Southgate Schools

Name
Class
Practice 5-4
Date
Factoring Quadratic Expressions
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Factor each expression completely.
1. x2 + 4x + 4
2. x2 - 7x + 10
3. x2 + 7x - 8
4. x2 - 6x
5. 2x2 - 9x + 4
6. x2 + 2x - 35
7. x2 + 6x + 5
8. x2 - 9
9. x2 - 13x - 48
10. x2 - 4
11. 4x2 + x
12. x2 - 29x + 100
13. x2 - x - 6
14. 9x2 - 1
15. 3x2 - 2x
16. x2 - 64
17. x2 - 25
18. x2 - 81
19. x2 - 36
20. x2 - 100
21. x2 - 1
22. 4x2 - 1
23. 4x2 - 36
24. 9x2 - 4
25. x2 - 7x - 8
26. x2 + 13x + 36
27. x2 - 5x + 6
28. x2 + 5x + 4
29. x2 - 21x - 22
30. x2 + 13x + 40
31. 2x2 - 5x - 3
32. x2 + 10x - 11
33. x2 - 14x + 24
34. 5x2 + 4x - 12
35. 2x2 - 5x - 7
36. 2x2 + 13x + 15
37. 3x2 - 7x - 6
38. 3x2 + 16x + 21
39. x2 + 5x - 24
40. x2 + 34x - 72
41. x2 - 11x
42. 3x2 + 21x
43. x2 + 8x + 12
44. x2 - 10x + 24
45. x2 + 7x - 30
46. x2 - 2x - 168
47. x2 - x - 72
48. 4x2 - 25
49. x2 - 121
50. x2 + 17x + 16
51. 10x2 - 17x + 3
52. 4x2 + 12x + 9
53. 4x2 - 4x - 15
54. 9x2 - 4
55. x2 + 6x - 40
56. 2x2 - 8
57. x2 + 18x + 77
58. 2x2 - 98
59. x2 + 21x + 98
60. x2 + 20x + 84
61. 9x2 + 30x + 16
62. 8x2 - 6x - 27
63. x2 - 3x - 54
64. x2 - 169
65. 25x2 - 9
66. 7x2 + 49
67. 2x2 - 10x - 28
68. x2 + 8x + 12
69. x2 - 2x - 35
70. x2 + 2x - 63
71. 20x2 - 11x - 3
72. 12x2 + 4x - 5
73. 4x2 - 5x - 6
74. 8x2 + 22x - 21
75. 3x2 - 3x - 168
Algebra 2 Chapter 5
Lesson 5-4 Practice
5
Name
Class
Date
Practice 6-2
Polynomials and Linear Factors
For each function, determine the zeros. State the multiplicity of any
multiple zeros.
1. y = (x - 5)3
2. y = x(x - 8)2
3. y = (x - 2)(x + 7)3
4. f(x) = x4 - 8x3 + 16x2
5. f(x) = 9x3 - 81x
6. y = (2x + 5)(x - 3)2
Write each function in standard form.
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7. y = (x - 5)(x + 5)(2x - 1)
8. y = (2x + 1)(x - 3)(5 - x)
9. A rectangular box is 24 in. long, 12 in. wide, and 18 in. high. If each
dimension is increased by x in., write a polynomial function in standard
form modeling the volume V of the box.
Write a polynomial function in standard form with the given zeros.
10. -1, 3, 4
11. 1, 1, 2
12. -3, 0, 0, 5
13. -2 multiplicity 3
Write each expression as a polynomial in standard form.
14. x(x - 1)2
15. (x + 3)2(x + 1)
16. (x + 4)(2x - 5)(x + 5)2
Write each function in factored form. Check by multiplication.
17. y = 2x3 + 10x2 + 12x
18. y = x4 - x3 - 6x2
19. y = -3x3 + 18x2 - 27x
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Find the zeros of each function. Then graph the function.
20. y = (x + 1)(x - 1)(x - 3)
21. y = (x + 2)(x - 3)
22. y = x(x - 2)(x + 5)
Find the relative maximum, relative minimum, and zeros of each function.
23. f(x) = x3 - 7x2 + 10x
24. f(x) = x3 - x2 - 9x + 9
Write each polynomial in factored form. Check by multiplication.
25. x3 - 6x2 - 16x
26. x3 + 7x2 + 12x
27. x3 - 8x2 + 15x
28. A rectangular box has a square base. The combined length of a side of
the square base, and the height is 20 in. Let x be the length of a side of
the base of the box.
a. Write a polynomial function in factored form modeling the volume
V of the box.
b. What is the maximum possible volume of the box?
Algebra 2 Chapter 6
Lesson 6-2 Practice
3
Name
Class
Date
Practice 6-3
Dividing Polynomials
Determine whether each binomial is a factor of x3 ± 3x2 – 10x – 24.
1. x + 4
2. x - 3
3. x + 6
4. x + 2
Divide using synthetic division.
5. (x3 - 8x2 + 17x - 10) (x - 5)
6. (x3 + 5x2 - x - 9) (x + 2)
7. (-2x3 + 15x2 - 22x - 15) (x - 3)
8. (x3 + 7x2 + 15x + 9) (x + 1)
10. (x3 - 5x2 - 7x + 25) (x - 5)
11. (x4 - x3 + x2 - x + 1) (x - 1)
12. ax4 1 53 x3 2 23 x2 1 6x 2 2b 4 ax 2 13 b
13. (x4 - 5x3 + 5x2 + 7x - 12) (x - 4)
14. (2x4 + 23x3 + 60x2 - 125x - 500) (x + 4)
Use synthetic division and the Remainder Theorem to find P(a).
15. P(x) = 3x3 - 4x2 - 5x + 1; a = 2
16. P(x) = x3 + 7x2 + 12x - 3; a = -5
17. P(x) = x3 + 6x2 + 10x + 3; a = -3
18. P(x) = 2x4 - 9x3 + 7x2 - 5x + 11; a = 4
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9. (x3 + 2x2 + 5x + 12) (x + 3)
Divide using long division. Check your answers.
19. (x2 - 13x - 48) (x + 3)
20. (2x2 + x - 7) (x - 5)
21. (x3 + 5x2 - 3x - 1) (x - 1)
22. (3x3 - x2 - 7x + 6) (x + 2)
23. y = x3 + 3x2 - 13x - 15; (x + 5)
24. y = x3 - 3x2 - 10x + 24; (x - 2)
Divide.
25. (6x3 + 2x2 - 11x + 12) (3x + 4)
26. (x4 + 2x3 + x - 3) (x - 1)
27. (2x4 + 3x3 - 4x2 + x + 1) (2x - 1)
28. (x5 - 1) (x - 1)
29. (x4 - 3x2 - 10) (x - 2)
30. (3x3 2 2x2 1 2x 1 1) 4 ax 1 13 b
31. A box is to be mailed. The volume in cubic inches of the box
can be expressed as the product of its three dimensions:
V(x) = x3 - 16x2 + 79x - 120. The length is x - 8. Find linear
expressions for the other dimensions. Assume that the width is
greater than the height.
4
Lesson 6-3 Practice
Algebra 2 Chapter 6
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Use synthetic division and the given factor to completely factor each
polynomial function.