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 - Section 6.5 - Synthetic Division and the Remainder Theorem - Exercise Set - Page 453: 21

Answer

$f(-3)=-133$

Work Step by Step

The remainder theorem: If the polynomial f(x) is divided by $x-c$, then the remainder is $f(c).$ Divide $3x^{3}-7x^{2}-2x+5$ with $x+3,\qquad (c=-3)$ $\begin{array}{rrrrrrrr} \underline{-3}| &3 & -7 & -2 & 5 & & & & \\ & & -9 & 48 & -138 & & & & \\ & --& -- &-- &-- & & & & \\ &3 & -16 & 46 & -133 & & & & \end{array}$ Quotient = $ 3x^{2}-16x+46$ Remainder = $f(-3)=-133$
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