Galois Theory question

[Metric_Space]

Homework Statement

Let L/K be a Galois extension with Galois group isomorphic to A4. Let g(x) ϵ K [x] be an irreducible polynomial that is degree 3 that splits in L. Show that the Galois group of
g(x) over K is cyclic.

Homework Equations

The Attempt at a Solution

I know, Galois means normal and separable.

Irrdeducible poly of degree 3 that splits in L means it splits into linear factors.

ie. g(x)=(x-a1)*(x-a2)*(x-a3)

I am thinking Galois correspondence might come in handy, but not sure how...any ideas?

I'm not sure what information Cyclic gives.