Answer
$6p \left( 2p-1 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
12p^2-6p
,$ 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 $\{
12,-6
\}$ 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 $\{
p^2,p
\}$ is $
p
.$ Hence, the entire expression has $GCF=
6p
.$
Factoring the $GCF=
6p
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
6p \left( \dfrac{12p^2}{6p}-\dfrac{6p}{6p} \right)
\\\\=
6p \left( 2p-1 \right)
.\end{array}
