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 365: 74


The value of $k$ is $-12$

Work Step by Step

If $x-c$ is factor of $f\left( x \right)$, then $f\left( c \right)=0$ so, for $4x+3$ to be factor of $f\left( x \right)$: $f\left( \frac{-3}{4} \right)=0$. Thus, $\begin{align} & 20{{\left( \frac{-3}{4} \right)}^{3}}+23{{\left( \frac{-3}{4} \right)}^{2}}-10\left( \frac{-3}{4} \right)+k=0 \\ & \frac{-135}{16}+\frac{207}{16}+\frac{15}{2}+k=0 \\ & k=\frac{135-207-120}{16} \\ & k=\frac{-192}{16}=-12 \end{align}$ Therefore, the value of $k$ is $-12$.
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