Answer
$k=5$
Work Step by Step
The factor theorem says that if f(c)=0, then (x-c) is a factor of f(x) and if (x-c) is a factor of f(x), then f(c)=0.
Hence $f(2)=2^3-k2^2+2k+2=0\\8-4k+2k+2=0\\10-2k=0\\10=2k\\k=5$.
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 389: 107
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