Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter 2 - Section 2.4 - Dividing Polynomials; Remainder and Factor Theorems - Exercise Set - Page 364: 35

Answer

$f(-3)=-133$

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 $\{3,-7,-2,5\}$ 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 $f(x)=(3x^2-16x+46)(x+3)-133$; thus we have $f(-3)=-133$.

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