In the context of applying Eisenstein's Criterion to `f(x) = x^3 - 2`, what is the primary purpose of meticulously listing out all coefficients
`(a_3 = 1 , a_2 = 0 , a_1 = 0 , a_0 = -2)`:
A) To establish the exact degree of the polynomial, which is a prerequisite for determining if it is irreducible over `QQ`.
B) To ensure a comprehensive and accurate check against each of Eisenstein's specific divisibility conditions involving a chosen prime p, especially for coefficients that happen to be zero ?