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: 8

Answer

$y+2$

Work Step by Step

Factoring the expressions and cancelling the common factors between the numerator and the denominator, the given expression, $ (y^2+7y+10)\div(y+5) ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{y^2+7y+10}{y+5} \\\\= \dfrac{(y+5)(y+2)}{y+5} \\\\= \dfrac{(\cancel{y+5})(y+2)}{\cancel{y+5}} \\\\= y+2 .\end{array}
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