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 equation are roots of . Equivalently, can be divided by without a remainder,
where 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
, which is irreducible over a field 
,
is also a root of the equation 
in 
, then all the roots of the irreducible
equation 
are roots of 
. Equivalently, 
can be divided by 
without a remainder,
is also a polynomial over 
.
