C H A P T E R 2 Polynomial and Rational Functions

More documents

Recommendations

Info

244 Chapter 2 Polynomial and Rational Functions 49. 51. x 2 3x 1 ) 5x 3 13x 2 x 2 5x 3 15x 2 5x Thus, 5x3 13x 2 x 2 x 2 3x 1 5 x 2 50. 2 x 2 6x 2 2x 2 6x 2 0 5x 2. x 2 0x 2 ) x 4 3x 3 4x 2 6x 3 Thus, x4 3x 3 4x 2 6x 3 x 2 2 53. 2 6 6 Thus, x 4 0x 3 2x 2 6x 4 4x 3 27x 2 18x x 2 55. 4 2 57. 2 4 12 8 19 8 11 3x 3 2x 2 6x 3x 3 0x 2 6x 27 16 11 38 44 6 18 22 x 2 3x 2 52. 2 x 2 0x 3 4 2x 2 0x 4 1 x 2 3x 2 1 x 2 2 . 6x 3 8x 2 11x 4 8 x 2 . 24 24 Thus, 2x3 19x 2 38x 24 x 4 f x 20x 4 9x 3 14x 2 3x (a) (c) 1 20 Yes, x 1 is a zero of f. 0 20 20 20 9 0 9 9 20 11 14 0 14 0 14 11 3 Yes, x 0 is a zero of f. 3 0 3 0 8 8 2x 2 11x 6. 3 3 0 0 0 0 0 0 0 54. 56. (b) (d) x 2 1 ) 3x 4 0x 3 0x 2 0x 0 3x 4 3x 2 3x4 x2 1 3x2 3 3 x2 1 3x 2 3 3x 2 0 3x 2 3 2x2 0x 1 ) 6x4 10x3 13x2 3x 5x 2 2 5x 8 6x 4 0x 3 3x 2 6x 4 10x 3 13x 2 5x 2 2x 2 1 5 0.1 0.1 0.3 0.5 0.8 0 4 4 0.1x 3 0.3x 2 0.5 x 5 3 3 3 20 9 11 29 33 4 3x 3 20x 2 29x 12 x 3 3 4 20 20 Yes, x is a zero of f. 3 1 20 20 4 9 15 24 9 20 29 14 18 14 29 15 3 10x 3 16x 2 5x 10x 3 0x 2 5x 0.5 20 19.5 No, x 1 is not a zero of f. 4 16x 2 0x 2 16x 2 0x 8 10 3x 2 5x 8 10 2x 2 1 0.1x 2 0.8x 4 19.5 x 5 12 12 0 3x 2 11x 4 3 3 0 3 15 12 0 0 0 0 12 12
58. f x 3x (a) 4 3 8 20 16 12 16 16 3 4 4 0 3 8x2 20x 16 59. Yes, x 4 is a zero of f. (c) 2 3 3 8 20 16 2 4 16 3 6 24 0 f x x 4 10x 3 24x 2 20x 44 (a) Yes, x is a zero of f. 2 3 3 1 1 10 3 7 24 21 45 Thus, f 3 421. Thus, g2 0. 20 135 155 60. gt 2t (a) 4 2 5 0 0 8 52 208 2 13 52 208 Thus, g4 3276. (b) 2 2 5 22 2 5 22 5 5t4 8t 20 (e) 80 −8 5 −60 44 465 421 8 832 824 0 52 4 52 4 20 3296 3276 0 10 42 10 42 (b) (b) 4 3 1 1 1 3 f 1 9 10 1 9 Review Exercises for Chapter 2 245 8 12 20 No, x 4 is not a zero of f. (d) 1 3 8 20 16 3 11 9 3 11 9 25 8 102 8 102 No, x 1 is not a zero of f. 20 20 0 24 9 33 20 80 60 20 33 53 16 240 224 61. ; Factor: (a) Yes, is a factor of (b) The remaining factors of are and (c) f x x x 7x 1x 4 (d) Zeros: 7, 1, 4 3 4x2 x f x 7 x 1. 25x 28 2 f x x x 4 4 1 4 25 28 4 32 28 1 8 7 0 x 4 f x. 8x 7 x 7x 1 3 4x2 25x 28 62. (a) Yes, is a factor of (b) The remaining factors are and (c) (d) Zeros: x (e) 50 5 2x 2x 5 x 3. f x 2x 5x 3x 6 2 , 3, 6 2 f x 2x 6 2 11 21 90 12 6 90 2 1 15 0 x 6 f x. x 15 2x 5x 3 3 11x2 21x 90 −7 5 −100 44 53 9
Page 1 and 2:
CHAPTER 2 Polynomial and Rational F
Page 3 and 4:
9. (a) (c) 10. (a) (c) y 1 2 x2 (b
Page 5 and 6:
13. f x x 2 5 14. Vertex: Axis of
Page 7 and 8:
25. 27. 29. hx 4x 2 4x 21 Vertex
Page 9 and 10:
41. 2, 2 is the vertex. 42. 2, 0 is
Page 11 and 12:
61. fx 2x 10 2 7x 30 62. x-inter
Page 13 and 14:
75. —CONTINUED— (d) A 8 x50 x
Page 15 and 16:
86. (a) and (c) (b) (d) 1996 (e) Ve
Page 17 and 18:
Section 2.2 Polynomial Functions of
Page 19 and 20:
11. (a) (b) fx x4 fx x 3 3 4 y
Page 21 and 22:
Section 2.2 Polynomial Functions of
Page 23 and 24:
36. (a) 0 with multiplicity 2, 4 an
Page 25 and 26:
49. 51. 53. 55. 57. 59. 61. fx x
Page 27 and 28:
70. 72. 74. gx x 2 10x 16 x 2x
Page 29 and 30:
81. 83. 85. Zeros: 0, 2, 2 all of m
Page 31 and 32:
92. (a) 93. (c) 200 7 140 V 4 3r 3
Page 33 and 34:
111. 113. 115. 117. 12x 2 11x 5
Page 35 and 36:
2x 4 4. and y2 x 3 x (a) and (b
Page 37 and 38:
20. 22. 24. 26. 28. 29. 31. 33. 3 5
Page 39 and 40:
45. fx 4x (a) 1 4 0 13 4 4 4 4 9 3
Page 41 and 42:
58. f x 3x Factors: x 3, x 2 3
Page 43 and 44:
67. 69. 71. ht t 3 2t 2 7t 2 (a
Page 45 and 46:
79. 83. x n 3 ) x 3n 9x 2n 27x n
Page 47 and 48:
1. 4. 7. a 10 b 6 Section 2.4 Comp
Page 49 and 50:
52. 53. 55. 57. 59. 8 16i 2i 3i 4
Page 51 and 52:
74. 4.5x2 3x 12 0; a 4.5, b 3,
Page 53 and 54:
Section 2.5 Zeros of Polynomial Fun
Page 55 and 56:
18. 19. f x 3x 3 19x 2 33x 9 Po
Page 57 and 58:
−24 (c) Real zeros: 2, 1 145 ± 8
Page 59 and 60: 47. 48. fx 2x 3 3x 2 50x 75 Sin
Page 61 and 62: 54. f x x Since 1 3i is a zero, s
Page 63 and 64: 69. 71. 73. gx x 4 4x 3 8x 2 16
Page 65 and 66: 79. Let fx x4 gx 5x 2. 5 10x 5
Page 67 and 68: 99. fx x Rational zeros: 1 x 1 Ir
Page 69 and 70: 111. 9,000,000 0.0001x 2 60x 150,
Page 71 and 72: 129. 3 6i 8 3i 3 6i 8 3i 11
Page 73 and 74: 2 x x 2 7. fx 2 x x 2 Domain:
Page 75 and 76: 27. fx (a) Domain: all real number
Page 77 and 78: 35. gs (a) Domain: all real number
Page 79 and 80: 43. 45. f x 2x2 5x 2 2x 2 x 6
Page 81 and 82: 51. 53. 55. hx (a) Domain: all rea
Page 83 and 84: 60. gx (a) Domain: all real number
Page 85 and 86: 72. (a) x-intercepts: (b) 0 x 3
Page 87 and 88: 80. (a) 81. False. Polynomial funct
Page 89 and 90: 4. 5. 8. 10. 3x2 x2 < 1 4 (a) x 2
Page 91 and 92: 17. 19. 20. x 2 2x 3 < 0 18. x 3
Page 93 and 94: 25. 27. 29. 31. 4x 2 4x 1 ≤ 0 2
Page 95 and 96: 39. −2 −1 0 1 2 3 4 5 x Section
Page 97 and 98: Section 2.7 Nonlinear Inequalities
Page 99 and 100: 59. 61. x x x ≥ 0 x 5x 7 Critic
Page 101 and 102: 73. C 0.0031t 3 0.216t 2 5.54t
Page 103 and 104: Review Exercises for Chapter 2 1. (
Page 105 and 106: 9. 11. 13. hx 4x2 4x 13 10. f x
Page 107 and 108: 21. C 70,000 120x 0.055x The min
Page 109: 41. fx xx 3 x 2 5x 3 (a) The de
Page 113 and 114: 77. 79. 4 2 4 2 3i 2 1 i 2
Page 115 and 116: 97. Since is a zero, so is 3x 2x
Page 117 and 118: 111. 114. 117. f x Domain: all rea
Page 119 and 120: 4 126. hx x 1 (a) Domain: all rea
Page 121 and 122: 133. 135. fx 3x3 2x 2 3x 2 3x 2
Page 123 and 124: 142. 144. 146. 148. 12x 3 20x 2 <
Page 125 and 126: 3. V l w h x 2 x 3 x 2 x 3 2
Page 127 and 128: Problem Solving for Chapter 2 261 1
Page 129: 19. Use synthetic division to show
show all

C H A P T E R 2 Polynomial and Rational Functions

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?