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