The polynomial of degree 4, P(x)\displaystyle {P}{\left({x}\right)} has a root of multiplicity 2 at x=1\displaystyle {x}={1} and roots of multiplicity 1 at x=0\displaystyle {x}={0} and x=3\displaystyle {x}=-{3}. It goes through the point (5,512)\displaystyle {\left({5},{512}\right)}.
Find a formula for P(x)\displaystyle {P}{\left({x}\right)}.
P(x)=\displaystyle {P}{\left({x}\right)}=   ,