1. Find out all the zeroes of the polynomial and their multiplicity. Utilizes the fact above to find out the x-intercept which corresponds to each zero will cross the x-axis or only touch it and if the x-intercept will flatten out or not.
2. Find out the y-intercept, (0, P (0)) .
3. Utilizes the leading coefficient test to find out the behavior of the polynomial at the end of the graph.
4. Plot a few more points. It is left intentionally vague. The more points which you plot the better the sketch. At the least you must plot at least one at either end of the graph & at least one point among each pair of zeroes.
We must give a quick warning regarding this process before we really try to use it. This procedure supposes that all the zeroes are real numbers. If there are any complex zeroes then this procedure may miss some pretty significant features of the graph.