By Michael Holtfrerich

During this leap forward textual content, authors Holtfrerich and Haughn converse as academics, delivering passionate but sufferer emphasis on thoughts, yet now not on the rate of educating algebraic abilities. The authors construct on and attach issues via discussing the suggestions with scholars in a special but logical method. chatting with scholars as though they have been having a dialogue with them within the school room, the authors use universal, daily purposes that make experience to the typical pupil to illustrate thoughts. The authors' technique approximately the place and while issues could be coated is exclusive, as is the capstone bankruptcy on Modeling/Data research.

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4x 2 Ϫ 12x ϩ 9 60. 9x 2 ϩ 30x ϩ 25 61. 9x 2 ϩ 24xy ϩ 16y2 62. 25a2 Ϫ 60ab ϩ 36b2 63. 3x 2 ϩ 54x ϩ 243 64. 2y2 Ϫ 32y ϩ 128 65. x 2 Ϫ 18xy ϩ 81y2 66. x 2 ϩ 24xy ϩ 144y2 67. 4x 2 ϩ 28xy ϩ 49y2 68. 9a2 Ϫ 30ab ϩ 25b2 69. x 4 Ϫ 6x 2y ϩ 9y 2 70. a4 ϩ 10a2b ϩ 25b2 (71–86) Difference of Squares 71. x 2 Ϫ 36 72. y2 Ϫ 25 73. 4a2 Ϫ 25 74. 9b2 Ϫ 100 75. x 2 ϩ 9 76. 4y2 ϩ 25 77. 5a2 Ϫ 20 78. 7ay2 Ϫ 28a 79. 25x 2 Ϫ 36y2 80. 81a2 Ϫ 25b2 81. y4 Ϫ 64 82. a4 Ϫ 36 83. x 4 Ϫ 16 84. b4 Ϫ 81 85. x 4 Ϫ 13x 2 ϩ 36 86. y4 Ϫ 29y2 ϩ 100 (87–98) Sum and Difference of Cubes Answer Q6 This doesn’t factor.

We have to factor each denominator first in order to determine the LCD. a 2x 3x b Ϫ a 2 b x ϩ 3x Ϫ 10 x ϩxϪ6 Find the LCD 3 1x ϩ 521x Ϫ 221x ϩ 32 4 and multiply each fraction by the missing factor in its denominator. Next, subtract the numerators. ϭa 2x 3x b Ϫ a b 1x ϩ 521x Ϫ 22 1x Ϫ 221x ϩ 32 1x ϩ 32 3x bؒ 1x ϩ 521x Ϫ 22 1x ϩ 32 Ϫ a ϭa 1x Ϫ 321x ϩ 221x ϩ 32 ϭ 1x ϩ 321x ϩ 321x ϩ 221x Ϫ 22 ϭ xϪ3 1x ϩ 321x Ϫ 22 1x ϩ 52 2x b ؒ 1x Ϫ 221x ϩ 32 1x ϩ 52 3x 2 ϩ 9x b 1x ϩ 521x Ϫ 221x ϩ 32 Ϫ a The numerator factors, but not into any factors that would cancel with the denominator, so we are done.

X 2 Ϫ 24x ϩ 144 d. 4x 2 ϩ 12x ϩ 9 2. How many terms are in each polynomial expression? 29 30 Chapter 0 The Preliminaries 3. What is the name of the method you used to factor each polynomial expression? 4. Describe the steps you used. Member 4: Your task is to complete the following and then explain it to your group, making sure that everybody understands the technique you have mastered. Work alone until your instructor invites you to explain it to your other group members. 1. Completely factor each of the following polynomials: a.