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: 43


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

Work Step by Step

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