1. f(−3)=−412
2. The zeros are 2, –2, and –4.
3. There are no rational zeros.
4. The zeros are -4, 21, and 1.
5. f(x)=−21x3+25x2−2x+10
6. There must be 4, 2, or 0 positive real roots and 0 negative real roots. The graph shows that there are 2 positive real zeros and 0 negative real zeros.
7. 3 meters by 4 meters by 7 meters
Solutions to Odd-Numbered Exercises
1. The theorem can be used to evaluate a polynomial.
3. Rational zeros can be expressed as fractions whereas real zeros include irrational numbers.
5. Polynomial functions can have repeated zeros, so the fact that number is a zero doesn’t preclude it being a zero again.
7. –106
9. 0
11. 255
13. –1
15. –2, 1, 21
17. –2
19. –3
21. −25,6,−6
23. 2,−4,−23
25. 4, –4, –5
27. 5,−3,−21
29. 21,21+5,21−5
31. 23
33. 2, 3, –1, –2
35. 21,−21,2,−3
37. −1,−1,5,−5
39. −43,−21
41. 2,3+2i,3−2i
43. −32,1+2i,1−2i
45. −21,1+4i,1−4i
47. 1 positive, 1 negative
49. 3 or 1 positive, 0 negative
51. 0 positive, 3 or 1 negative
53. 2 or 0 positive, 2 or 0 negative
55. 2 or 0 positive, 2 or 0 negative
57. ±5,±1,±25
59. ±1,±21,±31,±61
61. 1,21,−31
63. 2,41,−23
65. 45
67. f(x)=94(x3+x2−x−1)
69. f(x)=−51(4x3−x)
71. 8 by 4 by 6 inches
73. 5.5 by 4.5 by 3.5 inches
75. 8 by 5 by 3 inches
77. Radius = 6 meters, Height = 2 meters
79. Radius = 2.5 meters, Height = 4.5 meters
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Precalculus.Provided by: OpenStaxAuthored by: Jay Abramson, et al..Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions.License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175..