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: 21


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

Work Step by Step

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