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: 28

Answer

$(v+9)(v-4)$

Work Step by Step

To factor a trinomial in the form $v^2+bv+c$, 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 $(v+\_)(v+\_)$. In the case of $v^2+5v-36$, we are looking for two numbers whose product is $-36$ and whose sum is $5$. The numbers $9$ and $-4$ meet these criteria because: $$9\times(-4)=-36\;\text{and}\;9+(-4)=5$$When we insert these numbers into the blanks, we arrive at the factors: $(v+9)(v-4)$.
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