3) Differentiation D: F[t] ---> F[t], is linear and satisfies Dt¹ = nt¹-1. It satisfies the usual rules for derivatives. Let f € F[t] be monic. We write f for Df. (a) Let c E F be a root of f. With p = t - c, show that f (c) #0 iff ep(f) = 1. Suppose that F contains Q, the rational numbers. (b) Show that gcd (f, f) = 1 iff Iff f = rad(f), ep(f) ≤1 i.e. V primes p of F[t]

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...