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: 23

Answer

$(x+12)(x-6)$

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 $x^2+6x-72$, we are looking for two numbers whose product is $-72$ and whose sum is $6$. The numbers $12$ and $-6$ meet these criteria, because $$12\times-6=-72\;\text{and}\;12+(-6)=6$$When we insert these numbers into the blanks, we arrive at the factors $(x+12)(x-6)$.
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