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: 24

Answer

$(x+7)(x-6)$

Work Step by Step

The 2 numbers whose product is $ac= 1(-42)=-15 $ and whose sum is $b= 1 $ are $\left\{ 7, -6 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ x^2+x-42 ,$ then the factored form is \begin{array}{l} x^2+7x-6x-42 \\\\= (x^2+7x)-(6x+42) \\\\= x(x+7)-6(x+7) \\\\= (x+7)(x-6) .\end{array}
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