Answer
$3(3m-2)^2$.
Work Step by Step
The given polynomial is
$=27m^2-36m+12$
Factor out $3$.
$=3(9m^2-12m+4)$
Write the the polynomial as $a^2-2ab+b^2$.
$=3((3m)^2-2(3m)(2)+2^2)$
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$
We have $a=3m$ and $b=2$.
$=3(3m-2)^2$
Hence, the factor of the given polynomial is $3(3m-2)^2$.
