Decide whether some given polynomials are irreducible over QQ

Decide whether the following polynomials are irreducible in $\mathbb{Q}[x]$.

1. $a(x) = x^3 + 2x^2 + 8x + 2$
2. $b(x) = x^3 + 2x^2 + 2x + 4$
3. $c(x) = x^3 + x^2 + x + 1$
4. $d(x) = x^3 + 14$
5. $e(x) = 5x^9 - 41$
6. $f(x) = x^2 + 5x + 25$
7. $g(x) = 5x^5 + 30x^4 + 42x^3 + 6x + 12$

1. $a(x)$ is Eisenstein at 2 and thus is irreducible.
2. $b(x) = (x^2+2)(x+2)$ is reducible.
3. $c(x) = (x^2+1)(x+1)$ is reducible.
4. $d(x)$ is Eisenstein at 7 and thus is irreducible.
5. $e(x)$ is Eisenstein at 41 and thus is irreducible.
6. $f(x-1) = x^2 + 3x + 21$ is Eisenstein at 3 and thus is irreducible. So $f(x)$ is also irreducible.
7. $g(x)$ is Eisenstein at 3 and thus is irreducible.