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 224: 13


Remainder = $0$ $(x-2)$ is a factor of $f(x)$ .

Work Step by Step

The Remainder Theorem states that when a function $f(x)$ is divided by $(x-R)$ , then the remainder will be: $f(R)$. Now, $f(2)=(3)(2^4)-(6)(2^3)-(5)(2)+10=(3)(16)-(6)(8)-(5)(2)+10=0$ The Factor Theorem states that if $f(a)=0$, then $(x-a)$ is a factor of $f(x)$ and vice versa. Therefore, by the Factor Theorem $(x-2)$ is a factor of $f(x)$ .
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