x+1 is a factor, because f(-1)=0.
From this factor we can divide to find the other factors through reducing the cubic to a quadratic. Normally a cubic has three roots, so the "multiplicity" is usually 3. Synthetic division by the root gives:
-1 | 1 -3 0...4
......1 -1 4..-4
......1 -4 4 | 0
We now have x^2-4x+4=(x-2)^2=0 so the two other roots coalesce as just one: x=2. Therefore, in this case the multiplicity of different roots is only 2, with x=-1 and 2 as the roots.