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: 24


quotient $x^4+7x^3+21x^2+60x+182$ and remainder $r(x)=\frac{549}{x-3}$

Work Step by Step

Step 1. The coefficients of the dividend can be identified as $\{1,4,0,-3,2, 3\}$ and the divisor is $x-3$; use synthetic division as shown in the figure to get the quotient and the remainder. Step 2. We can identify the result as $\frac{x^5+4x^3-3x^2+2x+3}{x-3}=x^4+7x^3+21x^2+60x+182+\frac{549}{x-3}$ with the quotient as $x^4+7x^3+21x^2+60x+182$ and the remainder as $r(x)=\frac{549}{x-3}$
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