Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Appendix - Synthetic Division - Exercises - Page 646: 27

Answer

no, $x=-2$ is NOT a solution

Work Step by Step

Using the Remainder Theorem, the remainder when $P(x)= 3x^3+2x^2-2x+11 ,$ is divided by $( x+2 )$ is given by $ P(-2) $. Substituting $x=-2$ in the function above results to \begin{align*} P(-2)&= 3(-2)^3+2(-2)^2-2(-2)+11 \\&= 3(-8)+2(4)-2(-2)+11 \\&= -24+8+4+11 \\&= -1 .\end{align*} Since the remainder (equal to $ -1 )$ is not zero, then $( x+2 )$ DOES NOT evenly divide $P(x)$. Hence, $ x=-2 $ is NOT a solution of $ 3x^3+2x^2-2x+11=0 $.
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