Let be a field and . Then is solvable by radicals if there exists a radical extension such that factors into linears when considered as an element of .
![$ f(x) \in F[x]$](http://images.planetmath.org:8080/cache/objects/9191/l2h/img2.png "$ f(x) \in F[x]$"){kind=small}
![$ K[x]$](http://images.planetmath.org:8080/cache/objects/9191/l2h/img6.png "$ K[x]$"){kind=small}