Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Find the real or imaginary solutions of each equation by factoring.

10. x 3 + 64 = 0 x cubed , plus 64 equals 0
11. x 3 − 1000 = 0 x cubed , minus , 1000 , equals 0
12. 125 x 3 − 27 = 0 125 x cubed . minus 27 equals 0
13. 64 x 3 − 1 = 0 64 x cubed , minus 1 equals 0
14. x 3 + 2 x 2 + 5 x + 10 = 0 x cubed , plus 2 , x squared , plus 5 x plus 10 equals 0
15. 6 x 2 + 13 x − 5 = 0 6 x squared , plus 13 x minus 5 equals 0
16. 0 = x 3 − 27 0 equals , x cubed , minus 27
17. 0 = x 3 − 64 0 equals , x cubed , minus 64
18. 8 x 3 = 1 8 x cubed , equals 1
19. 64 x 3 = − 8 64 x cubed , equals negative 8
20. x 4 − 10 x 2 = − 9 x to the fourth , minus , 10 x squared , equals negative 9
21. x 4 − 8 x 2 = − 16 x to the fourth , minus , 8 x squared , equals negative 16
22. x 4 − 12 x 2 = 64 x to the fourth , minus , 12 x squared , equals 64
23. x 4 + 7 x 2 = 18 x to the fourth , plus 7 , x squared , equals 18
24. x 4 + 4 x 2 = 12 x to the fourth , plus 4 , x squared , equals 12

See Problem 3.

Find the real solutions of each equation by graphing.

25. x 3 − 4 x 2 − 7 x = − 10 x cubed , minus , 4 x squared , minus 7 x equals negative 10
26. 3 x 3 − 6 x 2 − 9 x = 0 3 x cubed , minus , 6 x squared , minus 9 x equals 0
27. 4 x 3 − 8 x 2 + 4 x = 0 4 x cubed , minus , 8 x squared , plus 4 x equals 0
28. 6 x 2 = 48 x 6 x squared , equals 48 x
29. x 3 + 3 x 2 + 2 x = 0 x cubed , plus 3 , x squared , plus 2 x equals 0
30. 2 x 3 + 5 x 2 = 7 x 2 x cubed , plus 5 , x squared , equals 7 x
31. 4 x 3 = 4 x 2 + 3 x 4 x cubed , equals , 4 x squared , plus 3 x
32. 2 x 4 − 5 x 3 − 3 x 2 = 0 2 x to the fourth , minus , 5 x cubed , minus , 3 x squared , equals 0
33. x 2 − 8 x + 7 = 0 x squared , minus 8 x plus 7 equals 0
34. x 4 − 4 x 3 − x 2 + 16 x = 12 x to the fourth , minus , 4 x cubed , minus , x squared , plus 16 x equals 12
35. x 3 − x 2 − 16 x = 20 x cubed , minus , x squared , minus 16 x equals 20
36. 3 x 3 + 12 x 2 − 3 x = 12 3 x cubed , plus 12 , x squared , minus 3 x equals 12

See Problem 4.

Graphing Calculator Write an equation to model each situation. Then solve each equation by graphing.

37. The Johnson twins were born two years after their older sister. This year, the product of the three siblings ages is exactly 4558 more than the sum of their ages. How old are the twins?
38. The product of three consecutive integers is 210. What are the numbers?

B Apply

Solve each equation.

39. x 3 + 13 x = 10 x 2 x cubed , plus 13 x equals , 10 x squared
40. x 3 − 6 x 2 + 6 x = 0 x cubed , minus , 6 x squared , plus 6 x equals 0
41. 12 x 3 = 60 x 2 + 75 x 12 x cubed , equals , 60 x squared , plus 75 x
42. 125 x 3 + 216 = 0 125 x cubed . plus 216 equals 0
43. 81 x 3 − 192 = 0 81 x cubed , minus 192 equals 0
44. x 4 − 64 = 0 x to the fourth , minus 64 equals 0
45. − 2 x 4 − 100 = 0 negative 2 , x to the fourth , minus 100 equals 0
46. 27 = − x 4 − 12 x 2 27 equals negative , x to the fourth , minus , 12 x squared
47. x 5 − 5 x 3 + 4 x = 0 x to the fifth , minus , 5 x cubed , plus 4 x equals 0
48. 5 x 3 = 5 x 2 + 12 x 5 x cubed , equals , 5 x squared , plus 12 x
49. x 3 + x 2 + x + 1 = 0 x cubed , plus , x squared , plus x plus 1 equals 0
50. x 3 + 1 = x 2 + x x cubed , plus 1 equals , x squared , plus x

51. Think About a Plan The width of a plastic storage box is 1 ft longer than the height. The length is 4 ft longer than the height. The volume is 36  ft 3 . 36 , ft cubed . .  What are the dimensions of the box?

    • What is the formula for the volume of a rectangular prism?
    • What variable expressions represent the length, height, and width?
    • What equation represents the volume of the plastic storage box?
52. Error Analysis A student claims that 1, 2, 3, and 4 are the zeros of a cubic polynomial function. Explain why the student is mistaken.
53. Geometry The width of a box is 2 m less than the length. The height is 1 m less than the length. The volume is 60 m 3 . 60 , m cubed , .  What is the length of the box?

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