For example, has three factors with no duplicates. We say that each factor, , , and , has a multiplicity of 1. This results in a graph that looks a bit like a linear function near , , and when we zoom in on each of those places.

For , there are still three factors, but two of them are . This results in a graph that looks a bit like a quadratic near and a bit like a linear function near . We say that the factor has a multiplicity of 2 while the factor has a multiplicity of 1.

Now consider what the graph of would look like. The factors help us identify that the function has zeros at -3 and 4. We also know that since has a multiplicity of 1 and has a multiplicity of 3, the graph looks a bit like a linear polynomial crossing the -axis at -3 and a bit like a cubic polynomial crossing the -axis at 4. Since this is a 4th-degree polynomial with a positive leading coefficient, we know that as gets larger and larger in either the negative or positive direction, gets larger and larger in the positive direction.