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: 25


quotient $x^3-10x^2+51x-260$ and remainder $r(x)=\frac{1300}{x+5}$

Work Step by Step

Step 1. The coefficients of the dividend can be identified as $\{1,-5,1,-5,0\}$ and the divisor is $x+5$; use synthetic division as shown in the figure to get the quotient and the remainder. Step 2. We can identify the result as $\frac{x^4-5x^3+x^2-5x}{x+5}=x^3-10x^2+51x-260+\frac{1300}{x+5}$ with the quotient as $x^3-10x^2+51x-260$ and the remainder as $r(x)=\frac{1300}{x+5}$
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