I am trying to get some help on these problems

1. alpha = 7 + sqrt(23), B = sqrt(alpha)

Q: Find polynomials in I_{alpha, Q}

{Note: to find these polynomials, they have to have 7+sqt(23) as a root. Do you have any advice on how to find a polynomial that has this as a root

2. Prove that p in K[X] is irreducible if and only if <p(x)> is a maximal ideal in K[X]