 By iterating the above construction, one can construct a splitting field of any polynomial from "K"["X"].This is an extension field "L" of "K" in which the given polynomial splits into a product of linear factors.If "p" is any prime number and "n" is a positive integer, we have a finite field GF("pn") with "pn" elements; this is an extension field of the finite field formula_27 with "p" elements.