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: 48

Answer

$(t-16)(t-9)$

Work Step by Step

In decreasing order of exponents, the given expression, $ 144-25t+t^2 ,$ is equivalent to \begin{array}{l} t^2-25t+144 .\end{array} The 2 numbers whose product is $ac= 1(144)=144 $ and whose sum is $b= -25 $ are $\left\{ -16,-9 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} t^2-16t-9t+144 \\\\= (t^2-16t)-(9t-144) \\\\= t(t-16)-9(t-16) \\\\= (t-16)(t-9) .\end{array}
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