Answer:
The polynomial expression 
To ascertain the multiplicity of 0, -2, -4, 5.
The multiplicity refers to how many times a root appears in a function.
First, identify the function's roots by setting it to zero.

Thus, the roots are x=0, -2, -4, and 5
To determine the roots' multiplicities:
The factor of x will give a root of x=0 with a multiplicity of 1
likewise, x=-2 with a multiplicity of 3
x=-4 with a multiplicity of 2
and x=5 with a multiplicity of 4.