College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.4 - Page 388: 71

Answer

The constant term is a multiple of 3, The leading coefficient is a multiple of 4.

Work Step by Step

By the Rational Zero Theorem, if there is a rational root$, \displaystyle \frac{p}{q}$, of a polynomial equation, then p is a factor of the constant term, $a_{o}$ and q is a factor of the coefficient of the leading term $a_{n}$. -------------------- $\displaystyle \frac{p}{q}=\frac{3}{4}$ is a root. 3 is a factor of the constant term, 4 is a factor of the leading term. Or, The constant term is a multiple of 3, The leading coefficient is a multiple of 4.
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