By Ron Larson, Robert P. Hostetler

This market-leading textual content maintains to supply scholars and teachers with sound, continuously established factors of the mathematical suggestions. Designed for a two-term path, the recent 7th variation keeps the positive aspects that experience made Algebra and Trigonometry a whole answer for either scholars and teachers: fascinating functions, state of the art layout, and cutting edge expertise mixed with an abundance of conscientiously written workouts.

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**Example text**

S. households banking and paying bills online from 2002 through 2007. ϭ 2x ϩ 3. Example 1 Finding the Domain of an Algebraic Expression a. /Corbis is the set of all real numbers. In fact, the domain of any polynomial is the set of all real numbers, unless the domain is specifically restricted. b. The domain of the radical expression Ίx Ϫ 2 is the set of real numbers greater than or equal to 2, because the square root of a negative number is not a real number. c. The domain of the expression xϩ2 xϪ3 is the set of all real numbers except x ϭ 3, which would result in division by zero, which is undefined.

Rewrite 64 as 43. Factor. 40 Chapter P Prerequisites Trinomials with Binomial Factors To factor a trinomial of the form ax 2 ϩ bx ϩ c, use the following pattern. Factors of a ax2 ϩ bx ϩ c ϭ ͑x ϩ ͒͑x ϩ ͒ Factors of c The goal is to find a combination of factors of a and c such that the outer and inner products add up to the middle term bx. For instance, in the trinomial 6x 2 ϩ 17x ϩ 5, you can write all possible factorizations and determine which one has outer and inner products that add up to 17x.

5 5 ϭ because Ί125 64 4 4 3 3 ϭ 53 125 ϭ . 43 64 5 Ϫ32 ϭ Ϫ2 because ͑Ϫ2͒5 ϭ Ϫ32. d. Ί 4 Ϫ81 is not a real number because there is no real number that can be raised to the e. Ί fourth power to produce Ϫ81. Now try Exercise 65. 20 Chapter P Prerequisites Here are some generalizations about the nth roots of real numbers. Generalizations About nth Roots of Real Numbers Real Number a Integer n Root(s) of a Example a > 0 n > 0, n is even. n a, n a Ί ϪΊ 4 81 ϭ 3, 4 81 ϭ Ϫ3 Ί ϪΊ a > 0 or a < 0 n is odd.