An algebraic field extension \(L/K\) is normal if every irreducible polynomial \(p \in K[x]\) either has no roots in \(L\) or splits into linear factors in \(L[x]\).
What does it mean for a field extension $L/K$ to be normal?
What does an irreducible $p(x) \in K[x]$ do in a normal extension $L/K$?