Suppose we are given a polynomial, multiplied out, with highest power term axn. That is,
lower power terms.
Unlike rational functions, polynomials p(x) do not have asymptotes, so as x gets very large (or very negative), then p(x) must also get very large and positive, or large and negative. So no matter how much they wiggle in the middle, polynomials have one of the following four pairs of end-behaviors.

Borrowed from: C.A.T.S.
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