Question 1010315
The TWO imaginary zeros are 2i and -2i, giving the quadratic factor  {{{(x-2i)(x-(-2i))=(x-2i)(x+2i)=highlight_green(x^2+4)}}}.


Use polynomial division to obtain the degree three factor of the function, and use whatever you know to further factorize it, such as try Rational Roots Theorem and synthetic division to check possible roots.


The result from the polynomial division (process not shown here) is 
{{{f(x)=(x^2+4)(x^3-3x^2+x-3)}}}.


You now want to look for up to three possible real, rational roots among the possibilities of -1, -3, 1, 3.    The only one of those that worked was....
3, for the linear binomial factor  {{{x-3}}} and quotient  {{{x^2+1}}}.


The listing of these three other roots then is:
3, i, -i.