College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.3 - Dividing Polynomials - 3.3 Exercises - Page 309: 3

Answer

$\displaystyle \frac{2x^{2}-5x-7}{x-2}=2x-1+\frac{-9}{x-2}$

Work Step by Step

Using synthetic division, $ \left.\begin{array}{l} 2\lfloor \\ \\ \\ \end{array}\right. \begin{array}{rrr} 2 & -5 & -7\\\hline & 4 & -2\\\hline 2 & -1 & -9 \end{array} $ $Q(x)=2x-1, \quad R(x)=-9$ In the form $\displaystyle \frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)}$, $\displaystyle \frac{2x^{2}-5x-7}{x-2}=2x-1+\frac{-9}{x-2}$
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