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: 17

Answer

$(b-1)(b-4)$

Work Step by Step

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