Answer
$k=-12$
Work Step by Step
By the factor theorem, if $4x+3$ is a factor then $f(-\frac{3}{4})=0$. Thus $f(-\frac{3}{4})=20\cdot(-\frac{3}{4})^3+23(-\frac{3}{4})^2-10(-\frac{3}{4})+k=12+k=0$, so $k=-12$
College Algebra (6th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-32178-228-3
ISBN 13:
978-0-32178-228-1
Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.3 - Page 376: 74
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