We’re studying polynomial functions in my freshman Advanced Algebra course. I’ve been struggling with determining what it is they really need to know about polynomials. I’m not convinced that long division of polynomials is an essential enduring skill (feel free to try to convince me that I’m wrong). We now have CAS and W|A to do this. I do want them to be able to successively divide by linear factors to reduce a polynomial function to a product of linear factors and irreducible quadratics. Long dividing a 7th degree by a 5th degree? Eh.
So, I had to decide, what else do I want them to know? I have been talking to the pre-calc and calculus teachers to find out with what they struggle when they get to their courses. These are important conversations to have. We still have some work to do, but we’re getting there. In light of these conversations, I made this:
Among other things, I’m asking them to: identify the zeros, y-intercept, vertical scale factor and write the equation — determine if the function is decreasing faster between A & B or between H & I — determine the equation of the secant through C & G and through D & F — then for the big preview to calc piece: draw a tangent at E and determine which of those two secant’s slope better approximates the slope of the tangent. (link to .pdf or .docx).
Any suggestions for other questions I should be asking are welcome!