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 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 329: 15


a. The zeros of the function are: $\{-2,1+\sqrt 3i, 1-\sqrt 3i\}$ b. $P(x)=(x+2)(x^{2}-2x+4)$

Work Step by Step

(a) Zeros Factor the polynomial completely to obtain: $P(x)=x^{3}+8=(x+2)(x^{2}-2x+4)$ $x+2=0 \rightarrow x=-2$ $x^{2}-2x+4=0 \rightarrow x=1\pm\sqrt 3i$ Thus, the zeros of the function are: $\{-2,1+\sqrt 3i, 1-\sqrt 3i\}$ (b) Completely Factored Form From part (a) above, the completely factored form of P(x) is: $P(x)=(x+2)(x^{2}-2x+4)$
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