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: 12

Answer

$(x+4)(x+5)$

Work Step by Step

The 2 numbers whose product is $ac= 1(20)=20 $ and whose sum is $b= 9 $ are $\left\{ 4,5 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ x^2+9x+20 ,$ then \begin{array}{l}\require{cancel} x^2+4x+5x+20 \\\\= (x^2+4x)+(5x+20) \\\\= x(x+4)+5(x+4) \\\\= (x+4)(x+5) .\end{array}
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