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: 39

Answer

$(t+8)(t+4)$

Work Step by Step

In decreasing order of exponents, the given expression, $ 32+12t+t^2 ,$ is equivalent to \begin{array}{l} t^2+12t+32 .\end{array} The 2 numbers whose product is $ac= 1(32)=32 $ and whose sum is $b= 12 $ are $\left\{ 8,4 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} t^2+8t+4t+32 \\\\= (t^2+8t)+(4t+32) \\\\= t(t+8)+4(t+8) \\\\= (t+8)(t+4) .\end{array}
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