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 - Exercise Set: 79

Answer

$\frac{x^{2}}{3}-x+1$

Work Step by Step

We are given the expression $(\frac{2x^{2}}{3}-\frac{x}{6}+\frac{5}{6})-(\frac{x^{2}}{3}+\frac{5x}{6}-\frac{1}{6})$. We can subtract the second polynomial from the first polynomial by adding the opposite of the second polynomial to the first polynomial. $(\frac{2x^{2}}{3}-\frac{x}{6}+\frac{5}{6})+(-\frac{x^{2}}{3}-\frac{5x}{6}+\frac{1}{6})$ We can combine like terms to simplify. $(\frac{2x^{2}}{3}-\frac{x^{2}}{3})+(-\frac{x}{6}-\frac{5x}{6})+(\frac{5}{6}+\frac{1}{6})=\frac{x^{2}}{3}-\frac{6x}{6}+\frac{6}{6}=\frac{x^{2}}{3}-x+1$
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