Solution When looking at each factor, it is important to consider the multiplicity of the factor. For example, the factor \(x^3\) gives a zero at \(x=0\) with a multiplicity of 3. This detail means that the function will look somewhat cubic near \(x=0\). In a similar vein, the function will look linear near \(x=-5\) and quadratic near \(x=3\). Finally, this polynomial has degree 3+1+2=6 and has a positive leading coefficient, so the end behavior is up to the left and up to the right. With all of this information, you can sketch the graph. Here is the actual graph. I would expect the sketch to have much shorter min/maxes and you are not expected to know or precisely identify those for sketching.