Answer
$5(pt+6)(pt-1)$
Work Step by Step
Factoring the $GCF=
5
$, then the given expression, $
5p^2t^2+25pt-30
$ is equivalent to
\begin{array}{l}
5(p^2t^2+5pt-6)
.\end{array}
The two numbers whose product is $ac=
1(-6)=-6
$ and whose sum is $b=
5
$ are $\{
6,-1
\}$. Using these two numbers to decompose the middle term of the expression, $
5(p^2t^2+5pt-6)
,$ then the factored form is
\begin{array}{l}
5(p^2t^2+6pt-1pt-6)
\\\\=
5[(p^2t^2+6pt)-(1pt+6)]
\\\\=
5[pt(pt+6)-(pt+6)]
\\\\=
5[(pt+6)(pt-1)]
\\\\=
5(pt+6)(pt-1)
.\end{array}
