Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Chapter Review - Review Exercises - Page 268: 20

Answer

$x=2$ (multiplicity 2). $f(x) =(x-2)^2(x^2+5)$.

Work Step by Step

Step 1. List possible rational zeros $\frac{p}{q}:\pm1,\pm2,\pm4,\pm5,\pm10,\pm20$. Step 2. Use synthetic division as shown to find zero(s) $x=2$ (multiplicity 2). Step 3. Use the quotient to find other zero(s) $x^2+5=0$, no real solutions. Step 4. Thus $f(x)=x^4-4x^3+9x^2-20x+20=(x-2)^2(x^2+5)$.
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