What Icen said. If you take the roots of the constant (200), you get +/- 1, 2, 4, 5, 10, 20, 40, 50, 100. The factor(s) of the leading coefficient (x^4) is 1. So you divide the roots of the constant by the factor(s) of the leading coefficient. Then you use...what do you call that kind of division? Well, here's an example:
For -2
1 -2 17 -50 -200
-2 8 -50 200
-------------------------------
1 -4 25 -100 0
To do this, you take the coefficients in the equation starting with the leading coefficient. If there is a missing power of x (it doesn't go down chronologically), you substitute 0 for it. You take the number you're testing and multiply it by the first coefficient. Take that number and add it to the second coefficient. Repeat this. If you end up with a remainder of 0 at the end, then the number is a root.
When you have an unreal root (like the -5i that is given), then its conjugate is also a root.
It's 5 AM so sorry if my explanations are unclear or if I used the wrong terms, hehe.