How do you find a polynomial function that has zeros #x=-5, 1, 2# and degree n=4?
If a polynomial function
If these were its only factors, then it would be a cubic.
It is not clear from the question whether
In any case, a suitable quartic would be:
#f(x) = (x+5)^2(x-1)(x-2) = x^4+7x^3-3x^2-55x+50#