Answer
$(8t-9)(t-1)$
Work Step by Step
Rearranging the terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
9+8t^2-18t
\\\\=
8t^2-18t+9
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
8t^2-18t+9
\end{array} has $ac=
8(9)=72
$ and $b=
-18
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-9,-8
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
8t^2-9t-8t+9
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(8t^2-9t)-(8t-9)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
t(8t-9)-(8t-9)
.\end{array}
Factoring the $GCF=
(8t-9)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(8t-9)(t-1)
.\end{array}