Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.4 - Dividing Polynomials; Remainder and Factor Theorems - Exercise Set - Page 364: 37

Answer

$f(3)=240$
1581937300

Work Step by Step

Step 1. Based on the Remainder Theorem, the value of $f(c)$ can be obtained as the remainder of $f(x)$ divided by $x-c$. Step 2. The coefficients of the dividend $f(x)$ can be identified in order as $\{1,5,5,-5,-6\}$ and the divisor is $x-3$; use synthetic division as shown in the figure to get the quotient and the remainder. Step 3. We can identify the result as $f(x)=(x^3+8x^2+29x+82)(x-3)+240$; thus we have $f(3)=240$.
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