Find a third degree polynomial equation with rational coefficients that has roots - 4 and 6 i

One factor would be (x+4). Then you have (x - (6i)), or (x-6i). Since it is an imaginary solution, there is a positive and a negative version. So the third factor would be (x - (-6i)) or (x+6i). Then you multiply. (x-6i) (x+6i) is x^2+36. Multiply that by (x+4) and get a final answer of x^3+4x ^2+36x+144.