Answer
$4a(3a^2-6a+1)$
Work Step by Step
$12a^3-24a^2+4a$
$4a(3a^2-6a+1)$
The only pairs of numbers whose product is $3$ (the coefficient of $x^2$) are $1$ and $3$ or $−1$ and $−3$.
The only pairs of numbers whose product is $1$ (the value for c) are $1$ and $1$ or $−1$ and $−1$.
There is no combination of the pairs of numbers to get a value of $−6$, so we are at the factored form of the polynomial.