This is not a duplicate of theory of equations finding roots from given polynomial.
Given that the roots (both real and complex) of a polynomial are $\frac{2}{3}$, $-1$, $3+\sqrt2i$, and $3+\sqrt2i$, find the polynomial. All coefficients of the polynomial are real integer values.
What I have so far: $$(3x-2)(x+1)(x-\sqrt2\times i)=0$$ If I were solving other similar problems with two complex roots, I would probably be able to cancel them out, but I'm confused about how to do the $(x-\sqrt2i)$ part. Is this actually two complex roots that meet? Also, what degree is this polynomial? I would like an algebraic explanation please.