If P(x)=3x^{3}+x^{2}+48x+16 contains the factor x-4i, find all the remaining factors. Write p(x) in factored form.

So I have (x-4i) and (x+4i) as two factors which = (x^{2}+16)

I then divide using long polynomial division. (3x^{2}+x+48x+16)/(x+16) = 3x+1 with no remainders.

I find that (x-4i),(x+4i) and (3x+1) are all factors of the polynomial P(x).....Are these all the factors? Did I do this correctly?

Thank you very much