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Concept

Multiplicity of Zeros

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 are and In this case, even though there are three factors, there are only two unique zeros. Since can be factored twice in the polynomial, the zero has a multiplicity of Consider the graph of the polynomial function.

The graph of a polynomial function crosses the axis on zeros with an odd multiplicity. If the multiplicity of a zero is even, the graph only touches the axis.