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}
