Discovering the Intermediate Value Theorem

Here are a couple slides that my students filled out that (I hope) helped them understand how to apply IVT to verify if a real zero exists between two given x-values.  Click slides to enlarge.

Two things about "Theorems about Zeros of Polynomial Functions"

I'm prepping for a lecture called "Theorems about Zeros of Polynomial Functions."  With the exception of the Fundamental Theorem of Algebra and a couple results from said theorem, the lecture should really be called "Stuff That Became Extinct with the Graphing Calculator but We Make You Learn It Anyway."

Two Observations:

First, our text states the Rational Zero Theorem as follows:

 Just out of curiosity...why not write it more like the following:

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.

Personally, I've stopped using the scary polynomial function notation all together in my College Algebra classes.

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.