1. What is this problem about?
This problem allows us to see how polynomials behave at extremes, in the middle, where their highest and lowest points are, where their intercepts, under what intervals they are increasing or decreasing. But most of all the multiplicities of the zeroes show us how to act around the x-axis.
2. What do you need to pay special attention to in order to understand?
Be sure to pay attention to the leading coefficient and its exponent to make sure what direction(s) your end behavior will go off in. Also look at the multiplicities of your zero, these have everything to do with the graph. They determine whether the line will go through, bounce off, or curve through the x-axis. Make sure to find your y-intercept as that will also help develop the line.