Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 7 - Polynomial Equations and Factoring - 7.5 - Factoring x 2 + bx + c - Exercises - Page 390: 49

Answer

$(r+3s)(r+4s)$

Work Step by Step

To factor the polynomial $x^{2}+bx+c$ to $(x+p)$ and $(x+q)$, we need to have $p+q=b$ and $pq=c$. Similarly, to factor $r^{2}+7rs+12s^{2}$ to $(r+p)$ and $(r+q)$, we need to have $p+q=7s$ and $pq=12s^{2}$ $\implies p=3s$ and $q=4s$. Then, $r^{2}+7rs+12s^{2}=(r+3s)(r+4s)$
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