Bit of a tangent but the way polynomials are often introduced makes it difficult for kids to see why they matter so much. Polymials are usually taught as being

Bit of a tangent but the way polynomials are often introduced makes it difficult for kids to see why they matter so much. Polymials are usually taught as being the functions of the form f(x) = a_0 + a_1x + a_2x^2... a_nx^n, which can seem arbitrary. Why functions of that particular form? It becomes even less obvious when you talk about polynomials in multiple variables. But another way of putting it is that polynomials are the functions you can form from variables and constants using only the operations of addition and multiplication (a finite number of applications of them, that is, and including multiplication-by-self, i.e. exponentiation). Any such function can be expressed in the canonical polynomial form. If you put that way it's obvious how general and interesting polynomials are, and how the concept applies to multiple unknowns, not just one.