Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set: 31

Answer

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

Work Step by Step

In decreasing order of exponents, the given expression, $ x^2-72+6x ,$ is equivalent to \begin{array}{l} x^2+6x-72 .\end{array} The 2 numbers whose product is $ac= 1(-72)=-72 $ and whose sum is $b= 6 $ are $\left\{ 12,-6 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} x^2+12x-6x-72 \\\\= (x^2+12x)-(6x+72) \\\\= x(x+12)-6(x+12) \\\\= (x+12)(x-6) .\end{array}
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