Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write each polynomial in factored form. Check by multiplication.

7. x 3 + 7 x 2 + 10 x x cubed , plus 7 , x squared , plus 10 x
8. x 3 − 7 x 2 − 18 x x cubed , minus , 7 x squared , minus 18 x
9. x 3 − 4 x 2 − 21 x x cubed , minus , 4 x squared , minus 21 x
10. x 3 − 36 x x cubed , minus 36 x
11. x 3 + 8 x 2 + 16 x x cubed , plus 8 , x squared , plus 16 x
12. 9 x 3 + 6 x 2 − 3 x 9 x cubed , plus 6 , x squared , minus 3 x

See Problem 2.

Find the zeros of each function. Then graph the function.

13. y = ( x − 1 ) ( x + 2 ) y equals open x minus 1 close open x plus 2 close
14. y = ( x − 2 ) ( x + 9 ) y equals open x minus 2 close open x plus 9 close
15. y = x ( x + 5 ) ( x − 8 ) y equals x open x plus 5 close open x minus 8 close
16. y = ( x + 1 ) ( x − 2 ) ( x − 3 ) y equals open x plus 1 close open x minus 2 close open x minus 3 close
17. y = ( x + 1 ) ( x − 1 ) ( x − 2 ) y equals open x plus 1 close open x minus 1 close open x minus 2 close
18. y = x ( x + 2 ) ( x + 3 ) y equals x open x plus 2 close open x plus 3 close

See Problem 3.

Write a polynomial function in standard form with the given zeros.

19. x = 5 , 6 , 7 x equals 5 comma 6 comma 7
20. x = − 2 , 0 , 1 x equals negative 2 comma 0 comma 1
21. x = − 5 , − 5 , 1 x equals negative 5 comma negative 5 comma 1
22. x = 3 , 3 , 3 x equals 3 comma 3 comma 3
23. x = 1 , − 1 , − 2 x equals 1 comma negative 1 comma negative 2
24. x = 0 , 4 , − 1 2 x equals 0 comma 4 comma negative , 1 half
25. x = 0 , 0 , 2 , 3 x equals 0 comma 0 comma 2 comma 3
26. x = − 1 , − 2 , − 3 , − 4 x equals negative 1 comma negative 2 comma negative 3 comma negative 4

See Problem 4.

Find the zeros of each function. State the multiplicity of multiple zeros.

27. y = ( x + 3 ) 3 y equals . open x plus 3 close cubed
28. y = x ( x − 1 ) 3 y equals . x open x minus 1 close cubed
29. y = 2 x 3 + x 2 − x y equals , 2 x cubed , plus , x squared , minus x
30. y = 3 x 3 − 3 x y equals , 3 x cubed , minus 3 x
31. y = ( x − 4 ) 2 y equals open x minus 4 , close squared
32. y = ( x − 2 ) 2 ( x − 1 ) y equals open x minus 2 , close squared , open x minus 1 close
33. y = ( 2 x + 3 ) ( x − 1 ) 2 y equals open 2 x plus 3 close open x minus 1 , close squared
34. y = ( x + 1 ) 2 ( x − 1 ) ( x − 2 ) y equals open x plus 1 , close squared , open x minus 1 close open x minus 2 close

See Problem 5.

Find the relative maximum and relative minimum of the graph of each function.

35. f ( x ) = x 3 + 4 x 2 − 5 x f open x close equals , x cubed , plus 4 , x squared , minus 5 x
36. f ( x ) = − x 3 + 16 x 2 − 76 x + 96 f open x close equals negative , x cubed , plus , 16 x squared , minus 76 x plus 96
37. f ( x ) = − 4 x 3 + 12 x 2 + 4 x − 12 f open x close equals negative 4 , x cubed , plus , 12 x squared , plus 4 x minus 12
38. f ( x ) = x 3 − 7 x 2 + 7 x + 15 f open x close equals , x cubed , minus , 7 x squared , plus 7 x plus 15

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