Let f(x)=3x² +3x+9 (a) Determine whether f(x) is irreducible as a polynomial in Z/9Z[x]. If it is reducible, show the factorization. If it is irreducible, briefly explain why. (b) Determine the roots of f(x) as a polynomial in Z/9Z[x]. Why is this answer different from the factorization in the previous part? (c) Determine whether f(x) is irreducible as a polynomial in Q[x]. If it is reducible, show the factorization. If it is irreducible, briefly explain why. (d) Determine whether f(x) is irreducible as a polynomial in C[x]. If it is reducible, show the factorization. If it is irreducible, briefly explain why.