If one root of the equation , which is irreducible over a field ,
is also a root of the equation in , then all the roots of the irreducible
are roots of . Equivalently, can be divided by without a remainder,
is also a polynomial over .
More things to try:
Weisstein, Eric W. "Abel's Irreducibility Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbelsIrreducibilityTheorem.html