Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-5 Factoring x2+bx+c - Practice and Problem-Solving Exercises - Page 515: 25



Work Step by Step

To factor a trinomial in the form $w^2+bw+c$, 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 $(w+\_)(w+\_)$. In the case of $w^2-7w-8$, we are looking for two numbers whose product is $-8$ and whose sum is $-7$. The numbers $-8$ and $1$ meet these criteria because $$1\times(-8)=-8\;\text{and}\;1+(-8)=-7$$When we insert these numbers into the blanks, we arrive at the factors: $(w-8)(w+1)$.
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