The multiplicity of a zero of a polynomial function is how many times a particular number is a zero for a given polynomial.
For example, in the polynomial function [tex]f(x)=x(x+4)^2(x-2)^3[/tex], the zeros are 0 with a multiplicity of 1, -4 with a multiplicity of 2, and 2 with a multiplicity of 3.
Although this polynomial has only three zeros, we say that it has six zeros (or degree of 6) counting the multiplicities.
