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: 42

Answer

$(x+10)^2$

Work Step by Step

The 2 numbers whose product is $ac= 1(100)=100 $ and whose sum is $b= 20 $ are $\left\{ 10,10 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ x^2+20x+100 ,$ then the factored form is \begin{array}{l} x^2+10x+10x+100 \\\\= (x^2+10x)+(10x+100) \\\\= x(x+10)+10(x+10) \\\\= (x+10)(x+10) \\\\= (x+10)^2 .\end{array}
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