What's So Great About Polynomials?
American math education is notorious for introducing mathematical concepts long before it introduces the reason to care about them. Case in point: polynomials. You know them. They're the functions that look like this: $$f(x) = x^2 - x$$ or like this $$f(x) = -3x^3 + x^2 - \frac{1}{2} x - \pi.$$ You probably learned about these when you took Algebra. If you're like most students, you weren't immediately given a very good reason to care! In this post, I'll try to patch this hole by motivating polynomials for a student at a low level. They're not as unnatural as they might first appear; there is at least one good reason to care about polynomials! Writing Down Functions is Hard In your math education, you've probably spent a lot of time staring at weird functions like this: or this: or this: Drawing weird squiggly functions is easy. But what if you actually wanted to write one of these down ? Like, think about the function in the last picture he...