Okay, well, I am staring rather a bit confused at the definition of a polynomial,

f(x) = a_nx^n + a_n-1x^n-1 + ... + a_1x + a_0; and I believe I understand the exponents, for instance x^n-1, because they have to be getting progressively smaller either wise they would not be in order. But what truly confuses me is the subscripts, such as a_n or a_1. Could someone explain to me the reasoning behind the subscripts, thank you so very much.