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: 13



Work Step by Step

We are trying to fill in the blank in the equation $v^2+12v+20=(v+10)(v+\square).$ In order to do so, we will factor the trinomial on the left side of the equation, to determine the second factor. 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 $v^2+12v+20$, we are looking for two numbers whose product is $20$ and whose sum is $12$. The numbers $10$ and $2$ meet these criteria, because $$10\times(2)=20\;\text{and}\;10+(2)=12$$When we insert these numbers into the blanks, we arrive at the factors $(v+10)(v+2)$.
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