1. ## Writing Polynomial functions

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, ${P}{\left({x}\right)}$ has a root of multiplicity 2 at ${x}={4}$ and roots of multiplicity 1 at ${x}={0}$ and ${x}=-{3}$. It goes through the point ${\left({5},{24}\right)}$.
Find a formula for ${P}{\left({x}\right)}$.

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).

2. Originally Posted by xsavethesporksx
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, ${P}{\left({x}\right)}$ has a root of multiplicity 2 at ${x}={4}$ and roots of multiplicity 1 at ${x}={0}$ and ${x}=-{3}$. It goes through the point ${\left({5},{24}\right)}$.
Find a formula for ${P}{\left({x}\right)}$.

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).
$P(x) = kx(x+3)(x-4)^2$

$P(5) = 24$

solve for $k$