Polynomials are expressions where a variable is combined with coefficients and exponents in all sorts of exciting ways.
This is exciting. You should be semi-erect when reading this.
Yet despite their thrilling nature, polynomials (and their quadratic cousins) represent a pretty big roadblock for many students in high school, and everything related to them, including graphing, reducing, or just looking at them, is enough to cause a non-trivial number of people to break out into a rash.
Geek3 via Wikimedia Commons
The rate at which people become stricken by polynomial-induced rashes can probably be graphed as a polynomial, actually.
What They Say This Is Used For:
Really, polynomial relationships are fairly simple equations that show up all the time in studies of natural systems, so anyone considering a career in science, economics, statistics, or engineering will need to have a pretty good handle on what the deal is with these things.
"OK, no, that's ... a picture of a little man humping a function? Tony, were your parents the same person?"