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: 16


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

Work Step by Step

Step 1. Using long division as shown in the figure, we can obtain $\frac{2x^5-8x^4+2x^3+x^2}{2x^3+1}=x^2-4x+1+\frac{4x-1}{2x^3+1}$ Step 2. We can identify the quotient as $x^2-4x+1$ and the remainder as $r(x)=\frac{4x-1}{2x^3+1}$
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