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: 15

Answer

$(t-7)(t-2)$

Work Step by Step

The 2 numbers whose product is $ac= 1(14)=14 $ and whose sum is $b= -9 $ are $\left\{ -7,-2 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ t^2-9t+14 ,$ then the factored form is \begin{array}{l} t^2-7t-2t+14 \\\\= (t^2-7t)-(2t-14) \\\\= t(t-7)-2(t-7) \\\\= (t-7)(t-2) .\end{array}
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