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 - Page 255: 20



Work Step by Step

To factor a trinomial in the form $y^2+bx+c$, 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 $(y+\_)(y+\_)$. In the case of $y^2-y-30$, we are looking for two numbers whose product is $-30$ and whose sum is $-1$. The numbers $5$ and $-6$ meet these criteria because $$5\times-6=-30\;\text{and}\;5+(-6)=-1$$When we insert these numbers into the blanks, we arrive at the factors $(y+5)(y-6)$.
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