Name
Class
Date
Extra Practice
Chapter 5
Lesson 5-1
Write each polynomial in standard form. Then classify it by degree and by
number of terms.
1. a 2 1 4a 2 5a 2 2 a
24a2 1 3a; quadratic binomial
1
2. 3x 2 3 2 5x
22x 2 13 ; linear binomial
4. 15 2 y 2 2 10y 2 8 1 8y
2y 2 2 2y 1 7;
quadratic trinomial
5. 6c 2 2 4c 1 7 2 8c 2
22c 2 2 4c 1 7;
quadratic trinomial
3. 3n2 1 n3 2 n 2 3 2 3n3
22n 3 1 3n 2 2 n 2 3;
cubic polynomial of 4 terms
6. 3x 2 2 5x 2 x 2 1 x 1 4x
2x 2 ; quadratic monomial
Determine the end behavior of the graph of each polynomial function.
7. y 5 x 2 2 2x 1 3 (w, s)
8. y 5 2x 3 2 2x
9. y 5 7x 5 1 3x 3 2 2x (x, s)
(w, t)
1
1
10. y 5 2x 4 1 5x 2 2 2 (w, s) 11. y 5 15x 9 (x, s)
12. y 5 2x12 1 6x 6 2 36 (x, t)
Lesson 5-2
Write each polynomial in factored form. Check by multiplication.
13. x 3 1 5x
x(x 2 1 5)
14. x 3 1 x 2 2 6x
x(x 2 2)(x 1 3)
15. 6x 3 2 7x 2 2 3x
x(2x 2 3)(3x 1 1)
Write a polynomial function in standard form with the given zeros.
16. x 5 3, 2, 21
y 5 x 3 2 4x 2 1 x 1 6
17. x 5 1, 1, 2
y 5 x 3 2 4x 2 1 5x 2 2
19. x 5 1, 2, 6
y 5 x 3 2 9x 2 1 20x 2 12
20. x 5 23, 21, 5
y 5 x 3 2 x 2 2 17x 2 15
18. x 5 22, 21, 1
y 5 x 3 1 2x 2 2 x 2 2
21. x 5 0, 0, 2, 3
y 5 x 4 2 5x 3 1 6x 2
1
23. x 5 2, 4, 5, 7
24. x 5 22, 0, 3, 1
y 5 3x 4 1 2x 3 2 7x 2 1 2x
y 5 x 4 2 18x 3 1 115x 2 2 306x 1 280
22. x 5 22, 1, 2, 2
y 5 x 4 2 3x 3 2 2x 2 1 12x 2 8
Find the zeros of each function. State the multiplicity of multiple zeros.
25. y 5 (x 2 2)(x 1 4) 24, 2
26. y 5 (x 2 7)(x 2 3) 3, 7
27. y 5 (x 1 1)(x 2 8)(x 2 9) 21, 8, 9
28. y 5 x (x 1 1)(x 1 5) 25, 21, 0
29. y 5 x 2(x 1 1) 21, 0 (mult. 2)
30. y 5 (x 2 3)(x 2 4)2 3, 4 (mult. 2)
31. Find the relative maximum and minimum of the graph
of f (x) 5 x 3 2 3x 2 1 2. Then graph the function. 2, 22
f(x)
2
x
32. A jewelry store is designing a gift box. The sum of the length,
width, and height is 12 inches. If the length is one inch greater
the height, what should the dimensions of the box be to maximize
its volume? What is the maximized volume?
length: 3.52 in., height: 4.52 in., width: 3.96 in.; 63 in.3
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O
-2
2
Name
Class
Date
Extra Practice (continued)
Chapter 5
33. Tonya wants to make a metal tray by cutting four identical
x
square corner pieces from a rectangular metal sheet. Then
she will bend the sides up to make an open tray.
16 in.
x
a. Let the length of each side of the removed squares be x in.
x
Express the volume of the box as a polynomial function of x.
x
V(x) 5 4x 3 2 72x 2 1 320x
b. Find the dimensions of a tray that would have a 384-in.3
20 in.
not to scale
capacity. 2 in. high, 12 in. by 16 in. base or 4 in. high,
12 in. by 8 in. base
Lesson 5-3
Find the real or imaginary solutions of each equation by factoring.
34. x 3 1 27 5 0 23,
3 4 3i !3
2
37. x 2 1 400 5 40x 20
5
35. 8x 3 5 125 2,
25 4 5i !3
4
38. 0 5 4x 2 1 28x 1 49 27
2
5
36. 9 5 4x 2 2 16 42
39. 29x 4 5 248x 2 1 64
2 !6
3
Solve each equation.
40. t 3 2 3t 2 2 10t 5 0 0, 22, 5
41. 4m 3 1 m 2 2 m 1 5 5 0 21.25, 12 4 i !3
2
42. t 3 2 6t 2 1 12t 2 8 5 0 2
43. 2c 3 2 7c 2 2 4c 5 0 0, 212, 4
44. w 4 2 13w 2 1 36 5 0 43, 42
45. x 3 1 2x 2 2 13x 1 10 5 0 25, 1, 2
46. The product of three consecutive integers is 210. Use N to represent the
middle integer.
a. Write the product as a polynomial function of P(N).
Answers may vary: Sample:
P(N) 5 (N 2 1)N(N 1 1) 5 N 3 2 N
b. Find the three integers. 5, 6, 7
47. The product of three consecutive odd integers is 6783.
a. Write an equation to model the situation.
x(x 1 2)(x 1 4) 5 6783
b. Solve the equation by graphing to find the numbers. 17, 19, 21
Lesson 5-4
Determine whether each binomial is a factor of x 3 2 5x 2 2 2x 1 24.
49. x 2 3 yes
48. x 1 2 yes
50. x 1 4 no
Divide.
51. (x 3 2 3x 2 1 2) 4 (x 2 1) x 2 2 2x 2 2
52. (x 3 2 x 2 2 6x) 4 (x 2 3) x 2 1 2x
53. (2x 3 1 10x 2 1 8x) 4 (x 1 4) 2x 2 1 2x
54. (x 4 1 x 2 2 6) 4 (x 2 1 3) x 2 2 2
55. (x 2 2 4x 1 2) 4 (x 2 2)
x 2 2, R 22
56. (x 3 1 11x 1 12) 4 (x 1 3)
x 2 2 3x 1 20, R 248
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Name
Class
Date
Extra Practice (continued)
Chapter 5
Lesson 5-5
Find the roots of each polynomial equation.
57. x 3 1 2x 2 1 3x 1 6 5 0
22, 4i!3
58. x 3 2 3x 2 1 4x 2 12 5 0
3, 62i
59. 3x 4 1 11x 3 1 14x 2 1 7x 1 1 5 0
60. 3x 4 2 x 3 2 22x 2 1 24x 5 0
23, 0, 43, 2
21,
25 4 !13
6
2 1
61. 45x 3 1 93x 2 2 12 5 0 22, 25, 3
62. 8x 4 2 66x 3 1 175x 2 2 132x 2 45 5 0
214, 52, 3
Lesson 5-6
Find all the zeros of each function.
63. f (x) 5 x 3 2 4x 2 1 x 2 6 21, 2, 3
64. g(x) 5 3x 3 2 3x 2 1 x 2 1 1, 4i !3
3
65. h(x) 5 x 4 2 5x 3 2 8x 1 40 2, 5, 4i!3
66. f (x) 5 2x 4 2 12x 3 1 21x 2 1 2x 2 33
i !6
21, 3, 2 4 2
67. A block of cheese is a cube whose side is x in. long. You cut
off a 1-inch thick piece from the right side. Then you cut off
a 3-inch thick piece from the top, as shown at the right. The
volume of the remaining block is 2002 in.3. What are the
dimensions of the original block of cheese?
14 in. by 14 in. by 14 in.
68. You can construct triangles by connecting three vertices of
a convex polygon with n sides. The number of all possible
n 3 2 3n 2 1 2n
such triangles can be represented as f (n) 5
.
6
Find the value of n such that you can construct 84 such
triangles from the polygon. 9
Lesson 5-7
Use the Binomial Theorem to expand each binomial.
69. (x 2 1)3
x 3 2 3x 2 1 3x 2 1
81x 4
70. (3x 1 2)4
1 216x 3 1 216x 2 1 96x 1 16
71. (4x 1 10)3
64x 3 1 480x 2 1 1200x 1 1000
72. (x 1 2y)7
73. (5x 2 y)5
74. (x 2 4y 3)4
x7 1 14x 6y 1 84x 5y 2 1
3125x 5 2 3125x 4y 1 1250x 3y 2 2
x 4 2 16x 3y 3 1 96x 2y 6 2
4
3
3
4
2
3
4
5
280x y 1 560x y 1
250x y 1 25xy 2 y
256xy 9 1 256y 12
2
5
6
7
672x y 1 448xy 1 128y
75. The side length of a cube is given by the expression(2x 1 3y 2). Write a
binomial expression for the volume of the cube. 8x 3 1 36x 2y 2 1 54xy 4 1 27y 6
76. What is the sixth term in the binomial expansion of (3x 2 4)8 ? 1,548,288x 3
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Name
Class
Date
Extra Practice (continued)
Chapter 5
Lesson 5-8
Find a polynomial function whose graph passes through each set of points.
77. (2, 5) and (8, 11)
y5x13
78. (3, 23) and (7, 9)
y 5 3x 2 12
79. (22, 16) and (4, 13)
80. (21, 27), (1, 1), and (2, 21)
y 5 22x 2 1 4x 2 1
y5
212x
1 15
81. (1, 5), (3, 11), and (5, 5)
y5
232x 2
1 9x 2
82. (24, 213), (21, 2), (0, 21), and (1, 2)
5
2
y 5 x 3 1 3x 2 2 x 2 1
83. The table shows the annual population of Florida for selected years.
Year
1970
1980
1990
2000
Population (millions)
6.79
9.75
12.94
15.98
a. Find a polynomial function that best models the data. y 5 0.3076x 2 14.781
b. Use your model to estimate the population of Florida in 2020. 22.13 million
c. Use your model to estimate when the population of Florida will
reach 20.59 million. 2015
Lesson 5-9
Determine the cubic function that is obtained from the parent function y 5 x 3
after each sequence of transformations.
84. vertical stretch by a factor of 2;
85. vertical stretch by a factor of 3;
reflection across the x-axis;
horizontal translation 3 units left
vertical translation down 2 units;
horizontal translation 1 unit right
y 5 22(x 1 3)3
y 5 3(x 2 1)3 2 2
Find all the real zeros of each function.
86. y 5 2(x 2 3)3 1 2 2
87. 6(x 1 3)3 2 6 22
3
1
1
88. 23 ax 1 2 b 2 5 23
Find a quartic function with the given x-values as its only real zeros.
89. x 5 23 and x 5 3
y 5 x 4 2 81
92. x 5 28 and x 5 26
y 5 (x 1
7)4
21
90. x 5 1 and x 5 3
y 5 (x 2 2)4 2 1
93. x 5 22 and x 5 8
y 5 (x 2
3)4
2 625
91. x 5 0 and x 5 4
y 5 (x 2 2)4 2 16
94. x 5 23 and x 5 5
y 5 (x 2 1)4 2 256
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