- if a is a root of a polynomial, then this polynomial can be factored by (x-a)
- if a polynomial has rational coefficients, and a complex number as a root, then its conjugate is also a root.
So 1 is a root. Since it's a polynomial with rational coefficients, 3i is a root, but -3i too.
You've got the 3 roots, so now the polynomial will be in the form :