Precalc0006to0010-page1

Precalc0006to0010-page1 - a 1 , a 2 , , a n , are typically...

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(Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES • Be able to identify polynomial, rational, and algebraic expressions. • Understand terminology and notation for polynomials. PART A: DISCUSSION • In Chapters 1 and 2, we will discuss polynomial, rational, and algebraic functions, as well as their graphs. PART B: POLYNOMIALS Let n be a nonnegative integer. An n th -degree polynomial in x , written in descending powers of x , has the following general form : a n x n + a n ± 1 x n ± 1 + ... + a 1 x + a 0 , a n ² 0 () The coefficients , denoted by
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Unformatted text preview: a 1 , a 2 , , a n , are typically assumed to be real numbers, though some theorems will require integers or rational numbers. a n , the leading coefficient , must be nonzero , although any of the other coefficients could be zero (i.e., their corresponding terms could be missing). a n x n is the leading term . a is the constant term . It can be thought of as a x , where x = 1 . Because n is a nonnegative integer, all of the exponents on x indicated above must be nonnegative integers, as well. Each exponent is the degree of its corresponding term....
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This document was uploaded on 12/29/2011.

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