The polynomial of degree 5,
P
(
x
)
\displaystyle {P}{\left({x}\right)}
P
(
x
)
has leading coefficient 1, has roots of multiplicity 2 at
x
=
4
\displaystyle {x}={4}
x
=
4
and
x
=
0
\displaystyle {x}={0}
x
=
0
, and a root of multiplicity 1 at
x
=
−
2
\displaystyle {x}=-{2}
x
=
−
2
Find a possible formula for
P
(
x
)
\displaystyle {P}{\left({x}\right)}
P
(
x
)
.
P
(
x
)
=
\displaystyle {P}{\left({x}\right)}=
P
(
x
)
=
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