In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of the multiple angle identities. Please note that an arrow indicates a step in which quantities irrelevant to the extremization process are simply dropped; as examples, adding a constant term to a function doesn't change the domain positions of its extremes, nor does rescaling it by a positive factor. Rescaling by a negative factor of course exchanges its maximums and minimums.