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: 19

Answer

$(d-5)(d-2)$

Work Step by Step

The 2 numbers whose product is $ac= 1(10)=10 $ and whose sum is $b= -7 $ are $\left\{ -5,-2 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ d^2-7d+10 ,$ then the factored form is \begin{array}{l} d^2-5d-2d+10 \\\\= (d^2-5d)-(2d-10) \\\\= d(d-5)-2(d-5) \\\\= (d-5)(d-2) .\end{array}
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