Definition of a polynomial function

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.

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Originally Posted by Bashyboy

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 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.

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Don't be confused. It is just a way of naming.
It also helps to keep up with what goes with what.

In we have,
.

Note how the subscripts correspond to the exponents and coefficients.

Oh yes, thank you so much.