Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set - Page 371: 89

Answer

(i) $\dfrac{f(x)}{g(x)}=5x-1+\frac{6}{x}$ (ii) The domain of $\dfrac{f(x)}{g(x)}$ does not include 0.

Work Step by Step

Divide $f(x)$ by $g(x)$ to have: $\dfrac{f(x)}{g(x)} = \dfrac{25x^2-5x+30}{5x}$ $\dfrac{f(x)}{g(x)} = 5x-1+\frac{6}{x}$ Since $5x$ is in the denominator of the original quotient, and a denominator is not allowed to be zero, then $5x \ne 0 \\x \ne 0$
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