[tex]\begin{gathered} f(x)=(x\text{-3)}\cdot(x+2i)\cdot(x-2i) \\ f(x)=(x\text{-3)}\cdot(x^2-(2i)^2) \\ f(x)=(x\text{-3)}\cdot(x^2-(4i^2)) \\ f(x)=(x\text{-3)}\cdot(x^2-(-4)) \\ f(x)=(x\text{-3)}\cdot(x^2+4) \\ f(x)=(x^3+4x-3x^2-12) \end{gathered}[/tex]
Hence, it is the required polynomial.
