Hi Monica,
The key thing you may be missing is that non-real complex roots to a function always come in conjugate pairs. Thus, if f(-3-i) = 0, then f(-3+i) = 0 must also be true. From here you should plug in each of (-4), (-3-i), and (-3+i) and set each result equal to zero.
Note that when you plug in the complex roots, each of the real and imaginary components of the resulting expression should sum to zero, since f(-3 +/- i) = 0 = 0 + 0i. That is, you can group the real parts of the resulting expression and set them equal to zero and you can group the imaginary parts of the resulting expression and set them equal to zero. This should yield the four unique equations you need to solve for four unknown coefficients. (Each non-real root yields two equations but the real component equations from them repeat. The real root yields one equation).
Hope this helps, Let me know if you need further assistance.
Robert
