> Now - that said - a goal of many of our classes is also to prepare our students for success in whatever STEM courses follow in college, and some colleges may expect students to remember such details from a precalculus class,
I would hope that the Rational Zero Theorem is NOT one of those details. Suppose we create a polynomial of degree greater than 1 with integer coefficients but select those coefficients at random. The frequency of selecting coefficients of a polynomial with rational zeros is nearly ZERO. Then think about the fact that when polynomial functions are used as models for actual data, the coefficients are rarely integers. That is why the Rational Zero Theorem should be classified as one of the interesting antiques that used to occupy an inexcusably large portion of time in courses taught before calculus. Maybe that is why it disappeared from the AP Calculus course descriptions more than a decade ago.