Question 762649
Your found root of -2 is wrong.


You should find through Rational Roots Theorem and synthetic division, roots of -3, +1, and then you still would have a quadratic binomial of {{{(x^2+4)}}}.  Solving the equation {{{x^2+4=0}}} for x will give you {{{-2i}}} and {{{+2i}}}


Briefly, you should have made a process roughly equivalent to this:
Check for root -3;
Remainder 0, quotient {{{x^3-x^2+4x-4}}}
Check for root +1;
Remainder 0, quotient {{{x^2+4}}}
Solve the quadratic for its roots and find they are {{{-2i}}} and {{{2i}}}.