By Ron Larson
This market-leading textual content keeps to supply scholars and teachers with sound, continually established causes of the mathematical recommendations. Designed for a two-term path, the recent 8th version keeps the positive aspects that experience made Algebra and Trigonometry a whole resolution for either scholars and teachers: fascinating purposes, state-of-the-art layout, and cutting edge know-how mixed with an abundance of conscientiously written workouts.
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Additional resources for Algebra and Trigonometry (Eighth Edition)
7x Ϫ 2͒͑4x Ϫ 3͒ ͑x ϩ 10͒͑x Ϫ 10͒ 68. ͑2x ϩ 3͒͑2x Ϫ 3͒ ͑x ϩ 2y͒͑x Ϫ 2y͒ 70. ͑4a ϩ 5b͒͑4a Ϫ 5b͒ 2 ͑2x ϩ 3͒ 72. ͑5 Ϫ 8x͒ 2 ͑x ϩ 1͒ 3 74. ͑x Ϫ 2͒ 3 ͑2x Ϫ y͒ 3 76. ͑3x ϩ 2y͒ 3 3 2 ͑4x Ϫ 3͒ 78. ͑8x ϩ 3͒2 ͑x 2 Ϫ x ϩ 1͒͑x 2 ϩ x ϩ 1͒ ͑x 2 ϩ 3x Ϫ 2͒͑x 2 Ϫ 3x Ϫ 2͒ ͑Ϫx2 ϩ x Ϫ 5͒͑3x2 ϩ 4x ϩ 1͒ ͑2x2 Ϫ x ϩ 4͒͑x2 ϩ 3x ϩ 2͒ ͓͑m Ϫ 3͒ ϩ n͔͓͑m Ϫ 3͒ Ϫ n͔ ͓͑x Ϫ 3y͒ ϩ z͔͓͑x Ϫ 3y͒ Ϫ z͔ ͓͑x Ϫ 3͒ ϩ y͔2 86. ͓͑x ϩ 1͒ Ϫ y͔2 2 2 ͑2r Ϫ 5͒͑2r ϩ 5͒ 88. ͑3a 3 Ϫ 4b2͒͑3a 3 ϩ 4b2͒ 2 2 3 90. ͑5 t ϩ 4͒ ͑14 x Ϫ 5͒ 1 1 92. 5y Ϫ 3͒ 5x͑x ϩ 1͒ Ϫ 3x͑x ϩ 1͒ ͑2x Ϫ 1͒͑x ϩ 3͒ ϩ 3͑x ϩ 3͒ ͑u ϩ 2͒͑u Ϫ 2͒͑u 2 ϩ 4͒ ͑x ϩ y͒͑x Ϫ y͒͑x 2 ϩ y 2͒ 105.
XϪ1 b. 1 3xϪ2 c. 12a3bϪ4 4aϪ2b 2 Ϫ2 d. 3xy Solution 1 x a. xϪ1 ϭ Property 3 1 1͑x 2͒ x 2 ϭ ϭ Ϫ2 3x 3 3 3 Ϫ4 3 12a b 12a и a2 c. ϭ 4aϪ2b 4b и b4 The exponent Ϫ2 does not apply to 3. b. 2 Ϫ2 d. 3xy . b ϭ a Exponents and Radicals m Property 3 ϭ 3a5 b5 Property 1 ϭ 3Ϫ2͑x 2͒Ϫ2 yϪ2 Properties 5 and 7 ϭ 3Ϫ2xϪ4 yϪ2 Property 6 ϭ y2 32x 4 Property 3 ϭ y2 9x 4 Simplify. Now try Exercise 41. Scientific Notation HISTORICAL NOTE The French mathematician Nicolas Chuquet (ca. 1500) wrote Triparty en la science des nombres, in which a form of exponent notation was used.
Another way to factor the polynomial in Example 9 is to group the terms as follows. x3 Ϫ 2x2 ϭ͑ x3 Ϫ 3x͒ Ϫ ͑ ϭ x͑ Ϫ 3͒ Ϫ 2͑ ϭ͑ Ϫ 3͒͑x Ϫ 2͒ x2 x 3 Ϫ 2x 2 Ϫ 3x ϩ 6 ϭ ͑x 3 Ϫ 2x 2͒ Ϫ ͑3x Ϫ 6͒ Ϫ 3x ϩ 6 2x2 x2 Solution x2 Ϫ 6͒ Ϫ 3͒ As you can see, you obtain the same result as in Example 9. Group terms. ϭ x 2͑x Ϫ 2͒ Ϫ 3͑x Ϫ 2͒ Factor each group. ϭ ͑x Ϫ 2͒͑x 2 Ϫ 3͒ Distributive Property Now try Exercise 73. Factoring a trinomial can involve quite a bit of trial and error. Some of this trial and error can be lessened by using factoring by grouping.