ABSTRACT
Linear factors x−α of a polynomial P (x) with coefficients in a field k correspond precisely to roots α ∈ k of the equation P (x) = 0. This follows from unique factorization in the ring k[x]. [1] Here we also look at some special higher-degree polynomials, over finite fields, where we useful structural interpretation of the polynomials. [2]
Here we take for granted the existence of an algebraic closure k of a given field, as a fixed universe in which to consider roots of polynomial equations.
