Question

what is the polynomial function in factored form with zeros at 0, -3 and 4

Answer 1

What do you mean? In factored form this polymonial would be x(x+3)(x-4)=0. Those are the roots, but you already listed them so you answered your own question. Are you looking for the actual polynomial itself?

Answer 2

x(x+3)(x-4)=0. now just foil this out

Answer 3

If you are looking for the actual polynomial, it is a third degree and can be found doing what @liliy said.