I was able to create a polynomial function by just multiplying $\displaystyle -(x-3)(x-3)(x+1)(x-1)(x+2)(x-2)$ but I can't make it to where the y-intercept is at 3. Got any ideas?Design a polynomial function with the following characteristics. Show work.

- degree of 6
- four real zeros
- one real zero of multiplicity of 3
- y-intercept at 3
- behaves like $\displaystyle f(x) = -5x^6$ for large values of $\displaystyle |x|$ (end behavior)