Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises: 70

Answer

$\color{blue}{(m+5+n^2)(m+5-n^2)}$

Work Step by Step

Group the first three terms together to obtain: $=(m^2+10m+25)-n^4$ The trinomial is a perfect square trinomial in the form $a^2+2ab+b^2$ with $a=m$ and $b=5$. RECALL: $a^2+2ab+b^2=(a+b)^2$ Use the formula above to obtain: $=(m+5)^2-n^4 \\=(m+5)^2-(n^2)^2$ The polynomial above is a difference of two squares. Factor using the formula $a^2-b^2=(a+b)(a-b)$ with $a=m+5$ and $b=n^2$ to obtain: $=[(m+5)+n^2][(m+5)-n^2] \\=\color{blue}{(m+5+n^2)(m+5-n^2)}$
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