By Ron Larson
This market-leading textual content keeps to supply scholars and teachers with sound, continuously dependent factors of the mathematical suggestions. Designed for a two-term direction, the recent 8th variation keeps the gains that experience made Algebra and Trigonometry a whole resolution for either scholars and teachers: attention-grabbing purposes, state-of-the-art layout, and cutting edge know-how mixed with an abundance of rigorously written routines.
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Additional resources for Algebra and Trigonometry (Eighth Edition)
156. CAPSTONE Explain what is meant when it is said that a polynomial is in factored form. r (a) Factor the expression for the volume. (b) From the result of part (a), show that the volume of concrete is 2͑average radius͒͑thickness of the tank͒h. 157. Rewrite u6 Ϫ v6 as the difference of two squares. Then find a formula for completely factoring u 6 Ϫ v 6. Use your formula to factor x 6 Ϫ 1 and x 6 Ϫ 64 completely. 5 RATIONAL EXPRESSIONS What you should learn • Find domains of algebraic expressions.
5 2Ί3 b. 2 3 Ί 5 Solution a. b. 5 2Ί3 2 3 5 Ί ϭ Ί3 5 2Ί3 иΊ 3 Ί3 is rationalizing factor. ϭ 5Ί3 2͑3͒ Multiply. ϭ 5Ί3 6 Simplify. ϭ 2 3 5 Ί 3 52 Ί иΊ 3 52 3 52 is rationalizing factor. Ί ϭ 3 52 2Ί 3 Ί53 Multiply. ϭ 3 25 2Ί 5 Simplify. Now try Exercise 95. 2 Example 14 ϭ 23 Rationalizing a Denominator with Two Terms 2 2 ϭ 3 ϩ Ί7 3 ϩ Ί7 ϭ Exponents and Radicals и Multiply numerator and denominator by conjugate of denominator. 3 Ϫ Ί7 3 Ϫ Ί7 2͑3 Ϫ Ί7 ͒ 3͑3͒ ϩ 3͑ϪΊ7 ͒ ϩ Ί7͑3͒ Ϫ ͑Ί7 ͒͑Ί7 ͒ 2͑3 Ϫ Ί7 ͒ ͑3͒2 Ϫ ͑Ί7 ͒2 Use Distributive Property.
A) 750 1 ϩ 64. 68 ϫ 105͒5 In Exercises 65–70, evaluate each expression without using a calculator. 65. 66. 67. 68. (a) (a) (a) (a) 271͞3 32Ϫ3͞5 100Ϫ3͞2 1 Ϫ1͞3 69. (a) Ϫ 64 125 70. (a) Ϫ 27 3 (b) Ί 8 (b) 363͞2 16 Ϫ3͞4 (b) ͑81 ͒ 9 Ϫ1͞2 (b) ͑4 ͒ 1 Ϫ2͞5 (b) Ί32 1 Ϫ4͞3 (b) Ϫ 125 27 Ί9 Ϫ1͞3 In Exercises 71–76, use a calculator to approximate the number. ) 71. (a) Ί57 3 452 72. (a) Ί 73. 8 74. 2 2 75. 5 ϫ 109 76. 3 ϫ 104 (b) Ί (b) Ί9 ϫ 10Ϫ4 In Exercises 77 and 78, use the properties of radicals to simplify each expression.
Algebra and Trigonometry (Eighth Edition) by Ron Larson