College Algebra 9th txtbk

SECTION 4–1 Polynomial Functions, Division, and Models 275
15.
y
20.
y
5
3
5
5
x
3
3
x
5
3
16.
y
5
In Problems 21–24, list all zeros of each polynomial function, and
specify those zeros that are x intercepts.
5
5
x
21. P(x) x(x 2 9)(x 2 4)
22. P(x) (x 2 4)(x 4 1)
23. P(x) (x 5)(x 2 9)(x 2 16)
5
24. P(x) (x 2 5x 6)(x 2 5x 7)
In Problems 17–20, explain why each graph is not the graph of a
polynomial function.
y
17.
2
x
2
2
2
18.
y
5
In Problems 25–34, use algebraic long division to find the
quotient and the remainder.
25. (3x 2 5x 6) (x 1)
26. (2x 2 7x 4) (x 2)
27. (4m 2 1) (m 1)
28. (y 2 9) ( y 3)
29. (6 6x 8x 2 ) (x 1)
30. (11x 2 12x 2 ) (3x 2)
x 3 1
a 3 27
31. 32.
x 1
a 3
33. (3y y 2 2y 3 1) ( y 2)
34. (3 x 3 x) (x 3)
5
5
x
In Problems 35–40, divide using synthetic division.
35. (x 2 3x 7) (x 2)
5
36. (x 2 3x 3) (x 3)
37. (4x 2 10x 9) (x 3)
19.
3
y
38. (2x 2 7x 5) (x 4)
2x 3 3x 1
39. 40.
x 2
x 3 2x 2 3x 4
x 2
3
3
x
In Problems 41–44, is the given number a zero of the polynomial?
Use synthetic division.
41. x 2 4x 221; 17
3
42. x 2 7x 551; 29
43. 2x 3 38x 2 x 19; 19
44. 2x 3 397x 70; 14