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}
