Thank you for the opportunity to help you with your question!

The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0
zeroes 1, 3-2i (and 3+2i)
f(x) = (x-1)(x-(3-2i))(x-(3+2i)

Please let me know if you need any clarification. I'm always happy to answer your questions.