Answer
$x^4-4x^3-2x^2+20x$
Work Step by Step
Step 1. As $x=3+i$ is a zero, we know $x=3-i$ is also a zero.
Step 2. With all the 4 zeros, we have $f(x)=(x+2)(x)(x-3-i)(x-3+i)=x(x+2)[(x-3^2)^2+1]=(x^2+2x)(x^2-6x+10)=x^4-4x^3-2x^2+20x$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 3 - Polynomial and Rational Functions - Chapter Test - Page 270: 8
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