This is an example of the graphing of polynomials. In this example we introduce to the graph such things as zeroes (with multiplicities) and end behavior which give a better idea of how the graph should look like.
In this example we did not factor the polynomial because we still don't know how to factorize these but we started from the zeroes so its easy to find the polynomial. With the zeroes and the equation we can find the x and y intercepts. After finding these, we can find the maximums and minimums of the graph which in the the end is enough information for a fairly accurate graph.