These notes contain information regarding polynomials, zeros of polynomials and their multiplicity, graph of polynomials and long term behavior of polynomial functions:

The following 2 examples describe how to find the zeros of a polynomial function (Methods shown are factoring and factoring by grouping)

The next notes discuss multiplicity of zeros and the graphs of polynomials

Now that you understand the how the multiplicity of the zeros effects the dynamics of the graph of a polynomial, we can take a look at some examples where you are given a graph of a polynomial and have to find an equation to represent it.

The next examples ask you to find an equation of a polynomial of a function that goes through a specific point on the graph. These are similar to the ones you just did, however now you need to make sure the equation you come up with will go through the specified point.

Another example

The next examples describe the long term behavior of graphs. (I.e. What happens to the graphs as x goes to infinity or to negative infinity).