How do I find a polynomial function of degree three and has the zeros 2, - 1, and 3?

Answer: you can multiply it out.

Step-by-step explanation:

If any factor of a factored polynomial is zero, the whole polynomial is zero.

One factor has to be zero when x is 2. That factor is x-2. The others are x+1 and x-3.

The polynomial is (x-2) (x+1) (x-3). This is obviously a degree three polynomial, and it's zeros are obviously 2, - 1, and 3.