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: 8

Answer

$\pm 1, \pm 2, \pm 3, \pm4, \pm6, \pm12, \pm\frac{1}{2}, \pm\frac{1}{3}, \pm\frac{1}{6}, \pm\frac{2}{3}, \pm\frac{3}{2}, \pm\frac{4}{3}$

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 = $12$ leading coefficient = $6$ The factors of the constant term are: $\pm1, \pm2, \pm 3, \pm4, \pm6, \pm12$ The factors of the leading coefficient are: $\pm 1, \pm2, \pm3, \pm6$ Thus, the possible rational zeros of the given polynomial function are: $=\pm 1, \pm 2, \pm 3, \pm4, \pm6, \pm 12, \pm\frac{1}{2}, \pm \frac{1}{3}, \pm\frac{1}{6}, \pm\frac{2}{2}, \pm\frac{2}{3}, \pm\frac{2}{6}, \pm\frac{3}{2}, \frac{3}{3}, \pm\frac{3}{6}, \pm\frac{4}{2},\pm\frac{4}{3}, \pm\frac{4}{6}, \pm\frac{6}{2}, \pm\frac{6}{3}, \pm\frac{6}{6}, \pm\frac{12}{2}, \pm\frac{12}{2}, \pm\frac{12}{3}, \pm\frac{12}{6}$ Eliminate the duplicates to obtain: $\\=\pm 1, \pm 2, \pm 3, \pm4, \pm6, \pm12, \pm\frac{1}{2}, \pm\frac{1}{3}, \pm\frac{1}{6}, \pm\frac{2}{3}, \pm\frac{3}{2}, \pm\frac{4}{3},$
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