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: 42

Answer

$y^2+2y+4$

Work Step by Step

$y^3-8$ can be written as $y^3-2^3$, which is a difference of two cubes. RECALL: A sum or difference of two cubes can be factored using either of the following formulas: (1) $a^3+b^3=(a-b)(a^2-ab+b^2)$ (2) $a^3-b^3=(a-b)(a^2+ab+b^2)$ Using formula (2) above with $a=y$ and $b=2$ gives: $\dfrac{y^3-8}{y-2} \\= \dfrac{(y-2)(y^2+y(2)+2^2)}{y-2} \\=\dfrac{(y-2)(y^2+2y+4)}{y-2}$ Cancel out the common factor to obtain: $\require{cancel} \\=\dfrac{\cancel{(y-2)}(y^2+2y+4)}{\cancel{y-2}} \\=y^2+2y+4$
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