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: 30

Answer

$(x+12)(x-5)$

Work Step by Step

In decreasing order of exponents, the given expression, $ 7x-60+x^2 ,$ is equivalent to \begin{array}{l} x^2+7x-60 .\end{array} The 2 numbers whose product is $ac= 1(-60)=-60 $ and whose sum is $b= 7 $ are $\left\{ 12,-5 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} x^2+12x-5x-60 \\\\= (x^2+12x)-(5x+60) \\\\= x(x+12)-5(x+12) \\\\= (x+12)(x-5) .\end{array}
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