Remark

The polynomial

t = s_n-1X + s_n-2X² + ··· + s₀Xⁿ

can be obtained from s by allowing computations with X^-1. So far, X^-1 has no formal meaning (later, this will be remedied). But we can compute with it as if it is the inverse of X.

If we substitute X^-1 for X in s, then we find s(X^-1) = s_n-1X^1-n + s_n-2X^2-n + ··· + s₁X^-1 + s₀, and so Xⁿs(X^-1) is the required polynomial t.