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 - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 53

Answer

$ x=-2,-1$ and $x=1$ (multiplicity 2). $f(x)=(x+2)(x+1)(x-1)^2$

Work Step by Step

Step 1. For $f(x)=x^4+x^3-3x^2-x+2$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2$ Step 2. Use synthetic division to find one zero as shown in the figure to find a zeros $x=\pm1$. Step 3. Use the quotient to find other zeros: $x^2+x-2=0\Longrightarrow (x+2)(x-1)=0 \Longrightarrow x=-2,1$. Step 4. Factor the polynomial $f(x)=(x+2)(x+1)(x-1)^2$
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