Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.3 - Factoring Trinomials of the Form x^2+bx+x - Problem Set 6.3: 17

Answer

$(x+11y)(x-6y)$

Work Step by Step

To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$. In the case of $x^2+5xy-66y^2$, we are looking for two numbers whose product is $-66y^2$ and whose sum is $5y$. The numbers $11y$ and $-6y$ meet these criteria because $$11y\times-6y=-66y^2\;\text{and}\;11y+(-6y)=5y$$When we insert these numbers into the blanks, we arrive at the factors $(x+11y)(x-6y)$.
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