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: 52

Answer

$\left( x-\dfrac{1}{5}\right)^2$

Work Step by Step

The 2 numbers whose product is $ac= 1\left( \dfrac{1}{25} \right)=\dfrac{1}{25} $ and whose sum is $b= -\dfrac{2}{5} $ are $\left\{ -\dfrac{1}{5}, -\dfrac{1}{5} \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ x^2-\dfrac{2}{5}x+\dfrac{1}{25} ,$ then the factored form is \begin{array}{l} x^2-\dfrac{1}{5}x-\dfrac{1}{5}x+\dfrac{1}{25} \\\\= \left( x^2-\dfrac{1}{5}x \right) -\left( \dfrac{1}{5}x-\dfrac{1}{25}\right) \\\\= x\left( x-\dfrac{1}{5} \right) -\dfrac{1}{5}\left( x-\dfrac{1}{5}\right) \\\\= \left( x-\dfrac{1}{5}\right)\left( x-\dfrac{1}{5}\right) \\\\= \left( x-\dfrac{1}{5}\right)^2 .\end{array}
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