Degrees of terms in a polynomial

[Guv]

For many purposes, it is handy to be able to use expressions like the following

Polynomial(x) = Sum(A_j * x^j) for j = 0 to n

The above is a very compact notation for the following.

A₀ * x⁰ + A₁ * x¹ + A₂ * x² . . . + A_n * xⁿ, where A₀, A₁, A₂ et cetera are coefficients.

The compact notation requires us to think of the constant term as having zero as the exponent for x, and to think of the next term as having one as the exponent.

Does the above help any?