Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Test - Page 499: 18

Answer

$12$.

Work Step by Step

By the Remainder Theorem, if $f(x)$ is divided by $x-c$, then the remainder is $f(c)$. So if $f(x)$ is divided by $x+2$, then the remainder is $f(-2)$, the value of $c$ is in this case $-2$. Use synthetic division $\begin{matrix} -2) &1&-2&-11&5&34 \\ & &-2&8&6 &-22\\ & --&--&--& --&--\\ & 1&-4&-3&11&12 ​\end{matrix}$ The remainder $12$, is the value of $f(-2)$. Check Replace $x$ with $-2$ in the given function. $f(-2)=(-2)^4-2(-2)^3-11(-2)^2+5(-2)+34$ Simplify. $f(-2)=16+16-44-10+34$ $f(-2)=66-54$ $f(-2)=12\checkmark$.
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