By Richard N. Aufmann, Vernon C. Barker, Richard D. Nation
Available to scholars and versatile for teachers, university ALGEBRA AND TRIGONOMETRY, 7th variation, makes use of the dynamic hyperlink among suggestions and functions to carry arithmetic to lifestyles. by means of incorporating interactive studying options, the Aufmann group is helping scholars to higher comprehend recommendations, paintings independently, and acquire higher mathematical fluency. The textual content additionally contains expertise positive factors to house classes that let the choice of utilizing graphing calculators. The authors' confirmed Aufmann Interactive technique permits scholars to attempt a ability because it is gifted in instance shape. This interplay among the examples and take a look at routines serves as a checkpoint to scholars as they learn the textbook, do their homework, or learn a piece. within the 7th version, assessment Notes are featured extra prominently during the textual content to assist scholars realize the most important prerequisite abilities had to comprehend new ideas.
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Additional info for College Algebra and Trigonometry
Also, we are concerned only with factoring over the integers. That is, we search only for polynomial factors that have integer coefficients. Greatest Common Factor The first step in the factorization of any polynomial is to use the distributive property to factor out the greatest common factor (GCF) of the terms of the polynomial. Given two or more exponential expressions with the same prime number base or the same variable base, the GCF is the exponential expression with the smallest exponent.
The following example shows the direction we can take to accomplish our goal. If the product property for exponential expressions is to hold for rational exponents, then for rational numbers p and q, b pb q = b p + q. For example, 91>2 # 91>2 must equal 91>2+1>2 = 91 = 9 Thus 91>2 must be a square root of 9. That is, 91>2 = 3. The example suggests that b1>n can be defined in terms of roots according to the following definition. Definition of b1/n If n is an even positive integer and b Ú 0, then b1>n is the nonnegative real number such that (b1>n)n = b.
We begin with the case of zero as an exponent. n Definition of b0 For any nonzero real number b, b0 = 1. EXAMPLE Note 3 0 a b = 1 4 30 = 1 Note that -70 = - (70) = - 1. - 70 = - 1 (a2 + 1)0 = 1 Now we extend the definition to include negative integers. Definition of b؊n If b Z 0 and n is a natural number, then b-n = 1 1 and -n = b n. bn b EXAMPLE 3-2 = 1 1 = 9 32 EXAMPLE 1 1 = 43 = 64 4-3 7 7 5-2 = 2 = 25 7-1 5 Evaluate an Exponential Expression Evaluate. a. b. c. (-24)( - 3)2 (-4)-3 (-2)-5 -p0 (continued) 18 CHAPTER P PRELIMINARY CONCEPTS Solution a.