Answer
$9(3p^2-p+2)$
Work Step by Step
Factoring the $GCF=
9
,$ the given expression, $
27p^2-9p+18
,$ is equivalent to
\begin{align*}
9(3p^2-p+2)
\end{align*}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression above has $ac=
3(2)=6
$ and $b=
-1
$
There are no two numbers with a product of $c$ and a sum of $b.$ Hence, the expression $
9(3p^2-p+2)
$ cannot be further factored.