First, our text states the Rational Zero Theorem as follows:
Personally, I've stopped using the scary polynomial function notation all together in my College Algebra classes.If f(x) is a polynomial with integer coefficients written in descending order and if p/q is a zero of f(x), then p is a factor of the constant term of f(x) and q is a factor of the leading coefficient.
Second Observation: Descartes' Rule of Signs. There's no need for me to say anything, I'll just copy what I found on PurpleMath.com:
Descartes' Rule of Signs is a useful help for finding the zeroes of a polynomial, assuming that you don't have the graph to look at. This topic isn't so useful if you have access to a graphing calculator because, rather than having to do guess-n-check to find the zeroes (using the Rational Root Test, Descartes' Rule of Signs, synthetic division, and other tools), you can just look at the picture on the screen.Bam.
This doesn't, however, change the fact that we still teach Descartes' Rule of Signs at my college. Right now, I show my students the following:
As you can see, with the exception of a few minor changes, I basically just copy what's in the text. There's got to be a better way. Please enlighten me.