hello I just started on these tonight and i understand all the terms but this one is tricky because it has to go through a specific point and i dont quite understand how to do it yet.

Any help is appreciated:

The polynomial of degree 4,

has a root of multiplicity 2 at

and roots of multiplicity 1 at

and

. It goes through the point

.

Find a formula for

.

My train of thought

P(x)=

(X-4)^2 Multiplicity of 2 and zeros at 4

(X) Multiplicity of 1 and zero at 0

(X+3) Multiplicity of 1 and zero at -3

When i graph it, i get a 4th degree polynominal that goes through (-3,0)(0,0) and bounces off (4,0) but does not go through (5,24) instead it goes through (5,40).