A polynomial function has a degree 4, a negative leading coefficient, and real zeros 3 with multiplicity 2, -2 with a multiplicity of 1, and -3 with a multiplicity of 1

p(x) = -n*(x - 3)^2*(x + 2)*(x + 3)

Step-by-step explanation:

For a polynomial whit roots a, b, c, d, e, ... (Where those numbers are not necessarly different)

We can write a polynomial with those roots as:

A*(x -a)*(x - b)*(x - c)*

Where A is a real number, and it's the leading coefficient (The coefficient that multiplies the highest power term)

In this case we have the roots:

3, 3, -2 and -3 (3 is two times, because it has a multiplicity of 2)

Then this polynomial can be written as:

A*(x - 3)*(x - 3)*(x + 2)*(x + 3)

And we know that the leading coefficient is negative, then we can write:

A = -n, where n > 0.

Then our polynomial is:

p(x) = -n*(x - 3)^2*(x + 2)*(x + 3)