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: 32


quotient $x^4-x^2+x+1$ and remainder $r(x)=\frac{3}{x-2}$

Work Step by Step

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