#### Answer

$3 \left( 3c+4d+1 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Get the $GCF$ of the given expression, $
9c+12d+3
.$ 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 terms is $
3
$ since it is the highest number that can evenly divide (no remainder) all the given terms. Factoring the $GCF=
3
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3 \left( \dfrac{9c}{3}+\dfrac{12d}{3}+\dfrac{3}{3} \right)
\\\\=
3 \left( 3c+4d+1 \right)
.\end{array}