## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

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