Question

write a polynomial of the smallest degree with roots 3,3i, and -3i

Answer 1

(x-3)(x-3i)(x+3i)

Foil this out, and you have your polynomial.

Answer 2

Hmm.. so a polynomial with roots a,b,c.. and so on is: (x-a)(x-b)(x-c)....=0

So, a polynomial with the roots stated above can be:
(x-3)(x-3i)(x+3i)=0

Answer 3

and as Alina says, FOIL and simplify it out.