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 3.4 - Real Zeros of Polynomials - 3.4 Exercises: 7

Answer

$-8, -4, -2, -1, 1, 2, 4, 8, -\frac{1}{2}, \frac{1}{2}$

Work Step by Step

RECALL: The possible rational zeros of a polynomial function is given by $\dfrac{p}{q}$ where: $p$ = factor of the constant term $q$ = factor of the leading coefficient The given polynomial function has: constant term = $-8$ leading coefficient = $2$ The factors of the constant term are: $\pm1, \pm2, \pm 4, \pm8$ The factors of the leading coefficient are: $\pm 1, \pm2$ Thus, the possible rational zeros of the given polynomial function are: $=\pm 1, \pm 2, \pm 4, \pm8, \pm\frac{1}{2}, \pm\frac{2}{2}, \pm \frac{4}{2}, \pm\frac{8}{2} \\=\pm 1, \pm 2, \pm 4, \pm8, \pm\frac{1}{2}, \pm1, \pm2, \pm4 $ Eliminate the duplicates to obtain: $\\=\pm 1, \pm 2, \pm 4, \pm8, \pm\frac{1}{2}$
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