Multiplicity of Zeros

A zero is essentially a solution, in the form of an x value, for a polynomial function. Polynomials have more than one zero, real or otherwise, but individual zeros can appear more than once. The number of times that a specific number appears as a zero for a polynomial is its multiplicity. Take this example problem:

Which factors into this:

So the zeros are:

The above polynomial has two zeros, each of which have a multiplicity of 1. Here is an example problem in which the zero(s) of the polynomial have a multiplicity greater than 1:

Which factors into:

Which factors into:

Giving the zeros:

The zeros for this polynomial are -4, and 2. -4 still has a multiplicity of 1, just like the previous problem, while 2 has a multiplicity of 2.

This video explains how to find zeros and their multiplicity as well as providing a refresher on factoring.

This is an excellent explanation(with pictures!) on zeros, multiplicity and how they affect end behavior on graphs.