54. f(x) = x4 - 3x3 – x² – 12x - 20 part (a) all real %3D (Hint: One factor is x2 + 4.) OsEO Finding the Zeros of a Polynomial Function In Exercises 55-60, use the given zero to find all the zeros of the function. Function Zero 55. f(x) = x3 -x2 + 4x - 4 56. f(x) 2i $7-40, phing ros in ne all = 2x3 + 3x2 + 18x + 27 57. g(x) = x³ – 8x² + 25x - 26 58. g(x) = x3 + 9x² + 25x + 17 3i %3D 3 + 2i -4 + i 59. h(x) = x4 – 6x3 + 14x² – 18x + 9 %3D 1- /2i -2+ 3i 60. h(x) = x4 + x³ – 3x² – 13x + 14 Finding the Zeros of a Polynomial Function In Exercises 61-72, write the polynomial as the product of linear factors and list all the zeros of the function. 61. f(x) = x² + 36 ith 1 a 62. f(x) = x² + 49 63. h(x) = x² – 2x + 17 64. g(x) = x² + 10x + 17 nts 65. f(x) = x4 – 16 66. f(y) = y4 – 256 ny 67. f(z) = z2 - 2z + 2 %3D 68. h(x) = x3 - 3x2 + 4x - 2 69. g(x) = x3 - 3x2 + x + 5 70. f(x) = x³ – x² + x + 39 %3D 71. g(x) = x4 – 4x3 + 8x² - 16x + 16 %3D 72. h(x) = x4 + 6x3 + 10x2 + 6x + 9 A Finding the Zeros of a Polynomial Function In Exercises 73-78, find ali the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to disregard any of the possible rational zeros that are obviously not zeros of the function. 73. f(x) = x³ + 24x² + 214x + 740 5s2 + 5 562 12s – 263 41. f(x) = x³ – x² + 25x : 43. (x) = x4 - 6x³ + 14x² - 45. f(x) = 3x* - 17x + 25x² + 23x – 22 25 47. f(x) = 2x4 + 2x3 - 49. f(x) = x3 + x² - 2x + 12 51. (a) (x² + 4)(x² – 2) (c) (x + 2i)(x – 2i)(x + /2)(x – /2) 53. (a) (x² – 6)(x² – 2x + 3) (-2,0) 2x2 + 2x - 4 -8- (b) (x² + 4)(x + /2)* - /2 rst four 117. f(x) = x V6(x - /6) (x2 - 2x + 3) 119. The func (b) (x + f(4) = (e) (x + J6)(x - J6)(x - 1- 2i)(x – 1 + Jzi) , 121. f(x) = x 123. (a) x² + 57. 2,3 ± 2i 59. 1, 3, 1 ± 2i 55. ±2i, 1 61. (x + 6i)(x – 6i); ±6i 63. (x - 1- 4i)(x – 1 + 4i); 1 ± 4i 65. (x - 2)(x + 2)(x – 2i)(x + 2i); ±2, ±2i 67. (z -1+ i)(z-1- i); 1 ± i 69. (x + 1)(x – 2 + i)(x – 2 – i); – 1, 2 ± i 71. (x – 2)²(x + 2i)(x - 2i); 2, ±2i 73. -10, - 7 + 5i Section 2 1. rational 5. Domain f(x) → 7. Domair flx) → f(x) → ero of Signs 77. –2, -}, ±i 75. -,1 + 3 49 45 9. Vertica 79. One positive real zero, no negative real zeros - 1 Horizo 81. No positive real zeros, one negative real zero 11. Vertica 83. Two or no positive real zeros, two or no negative real zeros 83. Two or no positive real zeros, one negative real zero 3 Horizc 93. – 13. Vertic 3 49 4 87-89. Answers will vary. 91. 15. Vertic 95. ±2, ±5 97. ±1, Horize 4. 102. c ". d 100. a 103. (a) 17. (a) D (b) y- 101. b 15- (c) V H 9. 9- 2x (d) 15-2x (b) V(x) = x(9 – 2x)(15 - 2x) Domain: 0 < x < 2 (c) 125 100