Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.4 - Dividing Polynomials; Remainder and Factor Theorems - Exercise Set - Page 364: 48

Answer

$x=-3,\frac{1}{2},2$
1581970973

Work Step by Step

Step 1. With the given graph, we can determine a solution of the equation as $x=-3$. Step 2. The coefficients of the dividend $f(x)=2x^3+x^2-13x+6$ can be identified in order as $\{2,1,-13,6\}$ and the divisor is $x+3$; use synthetic division as shown in the figure to get the quotient and the remainder. Step 3. We can identify the result as $f(x)=(2x^2-5x+2)(x+3)=(2x-1)(x-2)(x+3)$; thus we can find the zeros of $f(x)$ as $x=-3,\frac{1}{2},2$
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