The polynomial of degree 5,

Question

P
(
x
)
has leading coefficient 1, has roots of multiplicity 2 at
x
=
4
and
x
=
0
, and a root of multiplicity 1 at
x
=
−
1

Find a possible formula for
P
(
x
)
.

Answer 1

Fixing your post .....
The polynomial of degree 5,
P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 4 and x = 0,
and a root of multiplicity 1 at x = −1

Find a possible formula for P(x).
"multiplicity 2 at x = 4" ----> (x-4)(x-4)
"multiplicity 2 at x = 0" ---->(x)(x)
"multiplicity 1 at x = −1" ----> (x+1)

so P(x) = 1(x-4)(x-4)(x)(x)(x+1)
P(x) = x^2 (x+1)(x-4)^2