Additional Practice
Topic 8
Lesson 8-1
Write each polynomial in standard form. Then classify it by degree and by number of terms.
1. a2 + 4a - 5a2 - a
2. 3n2 + n3 - n - 3 - 3n3
3. 3x2 - 5x - x2 + x + 4x
Determine the end behavior of the graph of each polynomial function.
4. y = 7x5 + 3x3 - 2x
1
1
5. y = 2x 4 + 5x2 - 2
6. y = 15x9
Describe the shape of the graph of each cubic function including end behavior,
turning points, and increasing/decreasing intervals.
7. y = 3x3 + x2
1
8. y = 2x + x3
9. y = 2x3 - 4x2
Lesson 8-2
Simplify the each expressions.
(
) (
5
3
11. 1
z4 - z3 + 4z2 + 6 - 1
z2 - 1
z+2
4
4
2
13. (6p - 3)(4p2 - 2p + 8)
10. (3x 4 - 2x + x 2 - 1) + (2x 2 - x - 3)
12. (2m + 4)(3m - 6)
)
Lesson 8-3
Write each polynomial in factored form. Check by multiplication.
14. x3 + 5x
15. x3 + x2 - 6x
16. 6x3 - 7x2 - 3x
Write a polynomial function in standard form with the given zeros.
17. x = 3, 2, - 1
18. x = 1, 1, 2
19. x = - 2, - 1, 1
20. x = 1, 2, 6
21. x = - 3, - 1, 5
22. x = 0, 0, 2, 3
23. x = - 2, 1, 2, 2
24. x = 2, 4, 5, 7
25. x = - 2, 0, 3, 1
1
Find the zeros of each function. State the multiplicity of multiple zeros.
26. y = (x - 2)(x + 4)
27. y = (x - 7)(x - 3)
28. y = (x + 1)(x - 8)(x - 9)
29. y = x(x + 1)(x + 5)
30. y = x2(x + 1)
31. y = (x - 3)(x - 4)2
32. Find the relative maximum and minimum of the graph of f(x) = x3 - 3x2 + 2.
Then graph the function.
33. 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?
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Additional Practice
Additional Practice
Lesson 8-4
Find the real or imaginary solutions of each equation by factoring.
34. x3 + 27 = 0
35. 8x3 = 125
36. 9 = 4x2 - 16
37. x2 + 400 = 40x
38. 0 = 4x2 + 28x + 49
39. - 9x4 = - 48x2 + 64
40. t3 - 3t2 - 10t = 0
41. 4m3 + m2 - m + 5 = 0
42. t3 - 6t2 + 12t - 8 = 0
43. 2c3 - 7c2 - 4c = 0
44. w4 - 13w2 + 36 = 0
45. x3 + 2x2 - 13x + 10 = 0
Solve each equation.
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).
b. Find the three integers.
Lesson 8-5
Determine whether each binomial is a factor of x3 − 5x2 − 2x + 24.
47. x + 2
48. x - 3
49. x + 4
51. (x3 - x2 - 6x) , (x - 3)
52. (2x3 + 10x2 + 8x) , (x + 4)
Divide.
50. (x3 - 3x2 + 2) , (x - 1)
53.
(x4
+
x2
- 6) ,
(x2
+ 3)
54.
(x2
- 4x + 2) , (x - 2)
55. (x3 + 11x + 12) , (x + 3)
Lesson 8-6
Find all rational roots of each polynomial equation.
56. x3 + 2x2 + 3x + 6 = 0
59.
3x4
-
x3
-
22x2
+ 24x = 0
57. x3 - 3x2 + 4x - 12 = 0
60.
45x3
+
93x2
- 12 = 0
58. 3x4 + 11x3 + 14x2 + 7x + 1 = 0
61. 8x4 - 66x3 + 175x2 - 132x - 45 = 0
Lesson 8-7
Find all the zeros of each function. Write the polynomial in factored form and
identify the linear and quadratic factors.
62. f(x) = x3 - 6x2 + x - 6
63. g(x) = 3x3 - 3x2 + x - 1
64. h(x) = x4 - 5x3 - 8x + 40
65. 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 of 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?
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