Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 225: 110



Work Step by Step

The Remainder theorem states that the remainder of a function $f(x)$ after dividing by $(x-r)$ is $f(r)$. As per the given equation, when $f(x)=-3x^{17}+x^9-x^5+2x$ is divided by $x+1$, then by the remainder theorem $f(-1)$ represents the remainder of the function. We simplify the given equation as follows: $f(-1)=-3(-1)^{17}+(-1)^9-(-1)^5+2(-1) \\=3-1+1-2 \\=1$
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