Answer
$ 2y(y-3)^2$.
Work Step by Step
The given polynomial is
$= 2y^3-12y^2+18y$
Factor out $2y$.
$= 2y(y^2-6y+9)$
Write the the polynomial as $a^2-2ab+b^2$.
$= 2y(y^2-2(y)(3)+3^2)$
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$
We have $a=y$ and $b=3$.
$= 2y(y-3)^2$
Hence, the complete factor of the polynomial is $ 2y(y-3)^2$.
