In polynomial functions, the multiplicity of a zero is the number of times that a zero can be factored from a function. Using the Factor Theorem, it is possible to rewrite a polynomial as a multiplication of its factors. As an example, consider the following polynomial function. This function can be rewritten as follows. This means that the zeros of $p(x)$ are $1$ and $3.$ In this case, even though there are three factors, there are only two unique zeros. Since $1$ can be factored twice in the polynomial, the zero $x=1$ has a multiplicity of $2.$ Consider the graph of the polynomial function.

The graph of a polynomial function crosses the $x\text{-}$axis on zeros with an odd multiplicity. If the multiplicity of a zero is even, the graph only touches the $x\text{-}$axis.