Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 7 - Rational Functions - 7.2 Simplifying Rational Expressions - 7.2 Exercises - Page 576: 80

Answer

a) $\frac{6 x^2-47 x-8}{x-8}=6x+1$ b) $ (x-8)\cdot (6x+1)$

Work Step by Step

Given \begin{equation} \begin{aligned} \left(6 x^2-47 x-8\right) \div(x-8). \end{aligned} \end{equation} Use synthetic division. \begin{equation} \begin{array}{r|rrr} 8&6 & -47 & -8\\ & & 48 & 8\\ \hline &6& 1 & 0 \end{array} \end{equation} a) The solution is \begin{equation} \begin{aligned} \frac{6 x^2-47 x-8}{x-8}=6x+1. \end{aligned} \end{equation} b) The prime factor decomposition is $$ (x-8)\cdot (6x+1).$$
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