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: 31

Answer

quotient $2x^4-7x^3+15x^2-31x+64$ and remainder $r(x)=\frac{-129}{x+2}$
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Work Step by Step

Step 1. The coefficients of the dividend can be identified in order as $\{2,-3,1,-1,2,-1\}$ 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 $\frac{2x^5-3x^4+x^3-x^2+2x-1}{x+2}=2x^4-7x^3+15x^2-31x+64+\frac{-129}{x+2}$ with the quotient as $2x^4-7x^3+15x^2-31x+64$ and the remainder as $r(x)=\frac{-129}{x+2}$
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