Intermediate Algebra (6th Edition)

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

Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set: 44

Answer

$-\dfrac{x^6y^5}{7z^2}+\dfrac{x^3y^2}{7z}-\dfrac{x^3}{z^2}$

Work Step by Step

Divide each term of the dividend by the divisor to obtain: $\require{cancel} =\dfrac{x^6y^6}{-7yz^2}-\dfrac{x^3y^3z}{-7yz^2}+\dfrac{7x^3y}{-7yz^2} \\=-\dfrac{x^6y^6}{7yz^2}+\dfrac{x^3y^3z}{7yz^2}-\dfrac{7x^3y}{7yz^2} $ Cancel out common factors to obtain: $\require{cancel} \\=-\dfrac{x^6\cancel{y^6}y^5}{7\cancel{y}z^2}+\dfrac{x^3\cancel{y^3}y^2\cancel{z}}{7\cancel{y}\cancel{z^2}z}-\dfrac{\cancel{7}x^3\cancel{y}}{\cancel{7y}z^2} \\=-\dfrac{x^6y^5}{7z^2}+\dfrac{x^3y^2}{7z}-\dfrac{x^3}{z^2}$
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