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: 56

Answer

$x=-1,-\frac{1}{3}$. $f(x) =(3x+1)(x+1)(x^2+2)$

Work Step by Step

Step 1. For $f(x)=3x^4+4x^3+7x^2+8x+2$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm\frac{1}{3},\pm\frac{2}{3}$ Step 2. Use synthetic division as shown in the figure to find a zero(s) $x=-1,-\frac{1}{3}$. Step 3. Use the quotient to find other zeros: $3x^2+6=0$ no real solutions. Step 4. Factor the polynomial $f(x)=(x+\frac{1}{3})(x+1)(3x^2+6)=(3x+1)(x+1)(x^2+2)$
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