Since there are zeros at x = -3, x = 0, and x = 4, it could then be said that x+3 = 0, x = 0, and
x-4 = 0. Using that information, you can multiply them out to find the polynomial:
x(x+3)(x-4) = 0
(x²+3)(x-4) = 0
x³+4x²+3x-12 = 0
So the polynomial would be x³+4x²+3x-12