Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write each polynomial in standard form. Then classify it by degree and by number of terms.

8. 7 x + 3 x + 5 7 x plus 3 x plus 5
9. 5 − 3 x 5 minus 3 x
10. 2 m 2 − 3 + 7 m 2 m squared , minus 3 plus 7 m
11. − x 3 + x 4 + x negative , x cubed , plus , x to the fourth , plus x
12. − 4 p + 3 p + 2 p 2 negative 4 p plus 3 p plus , 2 p squared
13. 5 a 2 + 3 a 3 + 1 5 eh squared , plus 3 , eh cubed , plus 1
14. − x 5 negative , x to the fifth
15. 3 + 12 x 4 3 plus , 12 x to the fourth
16. 6 x 3 − x 3 6 x cubed , minus , x cubed
17. 7 x 3 − 10 x 3 + x 3 7 x cubed , minus , 10 x cubed , plus , x cubed
18. 4 x + 5 x 2 + 8 4 x plus , 5 x squared , plus 8
19. x 2 − x 4 + 2 x 2 x squared , minus , x to the fourth , plus , 2 x squared

See Problem 2.

Determine the end behavior of the graph of each polynomial function.

20. y = − 7 x 3 + 8 x 2 + x y equals negative 7 , x cubed , plus , 8 x squared , plus x
21. y = − 3 x + 6 x 2 − 1 y equals negative 3 x plus 6 . x squared , minus 1
22. y = 1 − 4 x − 6 x 3 − 15 x 6 y equals 1 minus 4 x minus , 6 x cubed , minus , 15 x to the sixth
23. y = 8 x 11 − 2 x 9 + 3 x 6 + 4 y equals , 8 x to the eleventh , minus , 2 x to the ninth , plus , 3 x to the sixth , plus 4
24. y = − x 5 − 15 x 7 − 4 x 9 y equals negative , x to the fifth , minus , 15 x to the seventh , minus , 4 x to the ninth
25. y = − 3 − 6 x 5 − 9 x 8 y equals negative 3 minus , 6 x to the fifth , minus , 9 x to the eighth
26. y = x 4 − 7 x 2 + 3 y equals , x to the fourth , minus , 7 x squared , plus 3
27. y = − 8 x 7 + 16 x 6 + 9 y equals negative 8 , x to the seventh , plus , 16 x to the sixth , plus 9
28. y = − 14 x 6 + 11 x 5 − 11 y equals negative 14 , x to the sixth , plus , 11 x to the fifth , minus 11
29. y = − x 3 − x 2 + 3 y equals negative , x cubed , minus , x squared , plus 3
30. y = x 3 − 14 x − 4 y equals , x cubed , minus 14 x minus 4
31. y = 5 − 17 x 7 + 9 x 10 y equals 5 minus , 17 x to the seventh , plus , 9 x to the tenth

See Problem 3.

Describe the shape of the graph of each cubic function by determining the end behavior and number of turning points.

32. y = 3 x 3 − x − 3 y equals , 3 x cubed , minus x minus 3
33. y = − 9 x 3 − 2 x 2 + 5 x + 3 y equals negative 9 , x cubed , minus , 2 x squared , plus 5 x plus 3
34. y = 10 x 3 + 9 y equals , 10 x cubed , plus 9
35. y = 3 x 3 y equals , 3 x cubed
36. y = − 4 x 3 − 5 x 2 y equals negative 4 , x cubed , minus , 5 x squared
37. y = 8 x 3 y equals , 8 x cubed

See Problem 4.

Determine the degree of the polynomial function with the given data.

38. x	− 2 negative 2	− 1 negative 1	0	1	2
    y	16	7	2	1	4

39. x	− 2 negative 2	− 1 negative 1	0	1	2
    y	− 15 negative 15	− 9 negative 9	− 9 negative 9	− 9 negative 9	− 3 negative 3

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