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 363: 27


quotient $x^4+x^3+2x^2+2x+2$ and remainder $r(x)=0$

Work Step by Step

Step 1. The coefficients of the dividend can be identified in order as $\{1,0,1,0,0,-2\}$ and the divisor is $x-1$; use synthetic division as shown in the figure to get the quotient and the remainder. Step 2. We can identify the result as $\frac{x^5+x^3-2}{x-1}=x^4+x^3+2x^2+2x+2+\frac{0}{x-1}$ with the quotient as $x^4+x^3+2x^2+2x+2$ and the remainder as $r(x)=0$
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