This problem is about graphing a polynomial, which included a y-intercept and x-intercepts (or zeroes) with multiplicities, and end behavior. When a polynomial is given, we first have to factor. With the help of multiplicities- the number of times a zero shows on a graph, it will help us determine how to graph the equation demonstrating how they behave at the extremas and in the middle.
While graphing polynomials, you should pay special attention to the zeroes and their multiplicity. Multiplicities determine how the middle of the graph looks like: multiplicities of one go through the graph, two bounce, and three curve. We also need to pay close attention to the end behavior so we know what direction our graph should start and end at.
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