Mathematical Science Algebra Polynomial Rings and Irreducibility Criteria

Let f(X) = X2 + X + 1 and g(X) = X2 + X - 2 be polynomials in  ℤ [X]. Which of the following statements are true?

1
For all prime numbers p, f (X) mod p is irreducible in (ℤ/pℤ) [X].
2
There exists a prime number p such that g(X) mod p is irreducible in
(ℤ/pℤ) [X].
3
g(X) is irreducible in ℚ[X].
4
f(X) is irreducible in ℚ[X].

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