Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.3 - Polynomials and Polynomial Functions - Graphing Calculator Explorations - Page 278: 1

Answer

$x^3-4x^2+7x-8$

Work Step by Step

Removing the parenthesis and then combining like terms, the given expression, $ (2x^2+7x+6)+(x^3-6x^2-14) ,$ is equivalent to \begin{array}{l}\require{cancel} 2x^2+7x+6+x^3-6x^2-14 \\= x^3+(2x^2-6x^2)+7x+(6-14) \\= x^3-4x^2+7x-8 .\end{array} Let \begin{array}{l}\require{cancel}Y_1= (2x^2+7x+6)+(x^3-6x^2-14) ,\\Y_2= x^3-4x^2+7x-8 .\end{array} Using a graphing calculator, the graphs of $Y_1$ (dotted graph) and $Y_2$ (solid graph) are shown below. Since the graphs overlap, then $Y_2$ is the correct simplification of $Y_1.$
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