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: 50

Answer

$x=-6,-\frac{1}{2},1$
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Work Step by Step

Step 1. With the given table, we can determine a solution of the equation as $x=-6$. Step 2. The coefficients of the dividend $f(x)=2x^3+11x^2-7x-6$ can be identified in order as $\{2,11,-7,-6\}$ and the divisor is $x+6$; use synthetic division as shown in the figure to get the quotient and the remainder. Step 3. We can identify the result as $f(x)=(2x^2-x-1)(x+6)=(2x+1)(x-1)(x+6)$; thus we can find the zeros of $f(x)$ as $x=-6,-\frac{1}{2},1$
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