Exercises 15.1, page 425

1. $- 25$ $- 25$
3. Coefficients $1 0 0 - 4 11, R = - 26$ $1 0 0 - 4 11, R = - 26$
5. 4
7. 33
9. $- 43$ $- 43$
11. 30
13. 16
15. 38
17. Yes
19. No
21. Yes
23. $x^{2} + 3 x + 2, R = 0$ $x^{2} + 3 x + 2, R = 0$
25. $x^{2} - 2 x + 5, R = - 16$ $x^{2} - 2 x + 5, R = - 16$
27. $p^{5} + 2 p^{4} + 4 p^{3} + 2 p^{2} + 2 p + 4, R = 2$ $p^{5} + 2 p^{4} + 4 p^{3} + 2 p^{2} + 2 p + 4, R = 2$
29. $x^{6} + 2 x^{5} + 4 x^{4} + 8 x^{3} + 16 x^{2} + 32 x + 64, R = 0$ $x^{6} + 2 x^{5} + 4 x^{4} + 8 x^{3} + 16 x^{2} + 32 x + 64, R = 0$
31. $x^{3} + x^{2} + 2 x + 1, R = 0$ $x^{3} + x^{2} + 2 x + 1, R = 0$
33. No
35. No
37. Yes
39. No
41. Yes
43. Yes
45. $2 x^{2} - 5 x + 1 - \frac{8}{x + 4}$ $2 x^{2} - 5 x + 1 - \frac{8}{x + 4}$
47. $(4 x^{3} + 8 x^{2} - x - 2) \div (2 x - 1) = 2 x^{2} + 5 x + 2;$ $(4 x^{3} + 8 x^{2} - x - 2) \div (2 x - 1) = 2 x^{2} + 5 x + 2;$ no, because the coefficient of x in $2 x - 1$ $2 x - 1$ is 2, not 1.
49. $- 7$ $- 7$
51. $x^{2} - (3 + j) x + 3 j, R = 0$ $x^{2} - (3 + j) x + 3 j, R = 0$
53. Yes, because both functions cross the x-axis at the same values.
55. $3 x^{2} - 8 a x + 5 a^{2}$ $3 x^{2} - 8 a x + 5 a^{2}$
57.
1. No
2. Yes
59. Yes

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Table of Contents for Exercises 15.1, page 425