A recent discussion with Mark Palko [scroll down to the comments at this link] reminds me that I think that polynomials are way way overrated, and I think a lot of damage has arisen from the old-time approach of introducing polynomial functions as a canonical example of linear regressions (for example). There are very few settings I can think of where it makes sense to fit a general polynomial of degree higher than 2. I think that millions of students have been brainwashed into thinking of these as the canonical functions and that this has caused endless trouble later on. I’m not sure how I’d change the high school math curriculum to deal with this, but I do think it’s an issue.
I hate polynomials