Answer
$(t-7)(t-2)$
Work Step by Step
The 2 numbers whose product is $ac=
1(14)=14
$ and whose sum is $b=
-9
$ are $\left\{
-7,-2
\right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $
t^2-9t+14
,$ then the factored form is
\begin{array}{l}
t^2-7t-2t+14
\\\\=
(t^2-7t)-(2t-14)
\\\\=
t(t-7)-2(t-7)
\\\\=
(t-7)(t-2)
.\end{array}