#### Answer

$6rt \left( r^2-5rt+3t^2 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
6r^3t-30r^2t^2+18rt^3
,$ get the $GCF.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
The $GCF$ of the constants of the terms $\{
6,-30,18
\}$ is $
6
$ since it is the highest number that can divide all the given constants. The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{
r^3t,r^2t^2,rt^3
\}$ is $
rt
.$ Hence, the entire expression has $GCF=
6rt
.$
Factoring the $GCF=
6rt
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
6rt \left( \dfrac{6r^3t}{6rt}-\dfrac{30r^2t^2}{6rt}+\dfrac{18rt^3}{6rt} \right)
\\\\=
6rt \left( r^2-5rt+3t^2 \right)
.\end{array}