By Ron Larson
This market-leading textual content keeps to supply scholars and teachers with sound, always dependent causes of the mathematical techniques. Designed for a two-term direction, the hot 8th version keeps the beneficial properties that experience made Algebra and Trigonometry a whole answer for either scholars and teachers: attention-grabbing functions, state-of-the-art layout, and leading edge know-how mixed with an abundance of conscientiously written routines.
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Extra info for Algebra and Trigonometry (Eighth Edition)
X2 ϩ 1͒4 Ϫ ͑x 2 ϩ 1͒5 2 89. 91. 93. 95. 97. 99. 101. 103. 105. 107. 109. 111. 113. 114. 115. 116. 117. 118. 119. (b) a is shown in the following figure. x x x x x 1 1 1 1 1 x (a) x x 1 b b (c) a a a a b b b b b (d) b b 1 1 1 1 b 121. 122. 123. 124. a 2 Ϫ b 2 ϭ ͑a ϩ b͒͑a Ϫ b͒ a 2 ϩ 2ab ϩ b 2 ϭ ͑a ϩ b͒ 2 a 2 ϩ 2a ϩ 1 ϭ ͑a ϩ 1͒ 2 ab ϩ a ϩ b ϩ 1 ϭ ͑a ϩ 1͒͑b ϩ 1͒ x 125. 126. 127. 128. 3x 2 ϩ 7x ϩ 2 ϭ ͑3x ϩ 1͒͑x ϩ 2͒ x 2 ϩ 4x ϩ 3 ϭ ͑x ϩ 3͒͑x ϩ 1͒ 2x 2 ϩ 7x ϩ 3 ϭ ͑2x ϩ 1͒͑x ϩ 3͒ x 2 ϩ 3x ϩ 2 ϭ ͑x ϩ 2͒͑x ϩ 1͒ 1 GEOMETRY In Exercises 129–132, write an expression in factored form for the area of the shaded portion of the figure.
X Ϫ 2͒͑2x͒ ϩ ͑x Ϫ 2͒͑3͒ Solution a. 6x 3 Ϫ 4x ϭ 2x͑3x 2͒ Ϫ 2x͑2͒ ϭ 2x͑ 3x 2 2x is a common factor. Ϫ 2͒ b. Ϫ4x 2 ϩ 12x Ϫ 16 ϭ Ϫ4͑x 2͒ ϩ ͑Ϫ4͒͑Ϫ3x͒ ϩ ͑Ϫ4͒4 ϭ Ϫ4͑ x2 Ϫ4 is a common factor. Ϫ 3x ϩ 4͒ c. ͑x Ϫ 2͒͑2x͒ ϩ ͑x Ϫ 2͒͑3͒ ϭ ͑x Ϫ 2͒͑2x ϩ 3͒ Now try Exercise 11. ͑x Ϫ 2͒ is a common factor. 38 Chapter P Prerequisites Factoring Special Polynomial Forms Some polynomials have special forms that arise from the special product forms on page 30. You should learn to recognize these forms so that you can factor such polynomials easily.
Some numbers have more than one nth root. For example, both 5 and Ϫ5 are square roots of 25. The principal square root of 25, written as Ί25, is the positive root, 5. The principal nth root of a number is defined as follows. Principal nth Root of a Number Let a be a real number that has at least one nth root. The principal nth root of a is the nth root that has the same sign as a. It is denoted by a radical symbol n a. Ί Principal nth root The positive integer n is the index of the radical, and the number a is the radicand.