Let f be a finite field of order q and let f(r) be a polynomial in flr] of degree n 1. prove that f[æ]/(f(r)) has q" elements. prove that if f(r) and g(r) arc p

Let F be a finite field of order q and let f(r) be a polynomial in Flr] of degree n 1. Prove that F[æ]/(f(r)) has q" elements. Prove that if f(r) and g(r) arc polynomials with rational coefficients whose