By Ron Larson, Robert P. Hostetler
This market-leading textual content keeps to supply scholars and teachers with sound, continually established motives of the mathematical innovations. Designed for a two-term direction, the hot 7th variation keeps the beneficial properties that experience made Algebra and Trigonometry a whole resolution for either scholars and teachers: fascinating purposes, state-of-the-art layout, and cutting edge expertise mixed with an abundance of conscientiously written routines.
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Extra resources for Algebra and Trigonometry (7th Edition)
For instance, a factoring model for 2 x 2 ؉ 3x ؉ 1 ͧ ؍2 x ؉ 1ͨͧx ؉ 1ͨ 43 Factoring Polynomials r 44 131. Chapter P x 8 x x x Prerequisites 132. x x x x x+3 18 4 5 5 (x 4 + 3) In Exercises 133–138, completely factor the expression. 133. 134. 135. 136. x4͑4͒͑2x ϩ 1͒3͑2x͒ ϩ ͑2x ϩ 1͒4͑4x3͒ x3͑3͒͑x2 ϩ 1͒2͑2x͒ ϩ ͑x2 ϩ 1͒3͑3x2͒ ͑2x Ϫ 5͒4͑3͒͑5x Ϫ 4͒2͑5͒ ϩ ͑5x Ϫ 4͒3͑4͒͑2x Ϫ 5͒3͑2͒ ͑x2 Ϫ 5͒3͑2͒͑4x ϩ 3͒͑4͒ ϩ ͑4x ϩ 3͒2͑3͒͑x2 Ϫ 5͒2͑x2͒ 137. ͑5x Ϫ 1͒͑3͒ Ϫ ͑3x ϩ 1͒͑5͒ ͑5x Ϫ 1͒2 138. ͑2x ϩ 3͒͑4͒ Ϫ ͑4x Ϫ 1͒͑2͒ ͑2x ϩ 3͒2 In Exercises 139–142, find all values of b for which the trinomial can be factored.
X 2 ϩ 5x ϩ 6 t2 Ϫ t Ϫ 6 24 ϩ 5z Ϫ z 2 x 2 Ϫ 13x ϩ 42 2x 2 Ϫ x Ϫ 1 12x 2 ϩ 7x ϩ 1 Ϫ5u 2 Ϫ 13u ϩ 6 In Exercises 71–78, factor by grouping. 71. 73. 75. 77. x 3 Ϫ x 2 ϩ 2x Ϫ 2 2x 3 Ϫ x 2 Ϫ 6x ϩ 3 6 ϩ 2x Ϫ 3x3 Ϫ x4 6x 3 Ϫ 2x ϩ 3x 2 Ϫ 1 72. 74. 76. 78. x 3 ϩ 5x 2 Ϫ 5x Ϫ 25 5x 3 Ϫ 10x 2 ϩ 3x Ϫ 6 x 5 ϩ 2x 3 ϩ x 2 ϩ 2 8x 5 Ϫ 6x 2 ϩ 12x 3 Ϫ 9 In Exercises 79–84, factor the trinomial by grouping. 79. 3x 2 ϩ 10x ϩ 8 81. 6x 2 ϩ x Ϫ 2 83. 15x 2 Ϫ 11x ϩ 2 80. 2x 2 ϩ 9x ϩ 9 82. 6x 2 Ϫ x Ϫ 15 84. 12x2 Ϫ 13x ϩ 1 In Exercises 85–120, completely factor the expression.
124. CAPSTONE A third-degree polynomial and a fourth-degree polynomial are added. (a) Can the sum be a fourth-degree polynomial? Explain or give an example. (b) Can the sum be a second-degree polynomial? Explain or give an example. (c) Can the sum be a seventh-degree polynomial? Explain or give an example. 50 25 x 20 30 40 50 60 Speed (in miles per hour) GEOMETRY In Exercises 117 and 118, use the area model to write two different expressions for the area. Then equate the two expressions and name the algebraic property that is illustrated.