Let f(x) be a polynomial of degree n in Z[x] with coefficients bounded by N. Prove that the algorithm described on page 189 to verify if f(x) is irreducible has complexity O(Nn). Prove the the Chinese...

Let f(x) be a polynomial of degree n in Z[x] with coefficients bounded by N. Prove that the algorithm described on page 189 to verify if f(x) is irreducible has complexity O(Nn). Prove the the Chinese remainder theorem for polynomials 4.6.1 stated on page 191. (Hint: follow the proof of the Chinese remainder theorem for integer numbers.)