Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

Chapter R - Elementary Algebra Review - R.5 Polynomials and Factoring - R.5 Exercise Set - Page 970: 25

Answer

$(m+15n)(m-10n)$

Work Step by Step

The given expression is equivalent to \begin{array}{l}\require{cancel} 5mn+m^2-150n^2 \\\\= m^2+5mn-150n^2 .\end{array} Using the factoring of trinomials in the form $x^2+bx+c,$ the given $\text{ expression }$ \begin{array}{l}\require{cancel} m^2+5mn-150n^2 \end{array} has $c= -150$ and $b= 5 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 15,-10 \right\}.$ Using these two numbers, the $\text{ expression }$ above is equivalent to \begin{array}{l}\require{cancel} (m+15n)(m-10n) .\end{array}

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