Show that for an element a in a field F
f(x) and f(x+a) have the samsame splitting field.
i want to get sure about my attempt :
without loss of generality suppose deg f is at least 1
then in the splitting field S of f
f(x)=(x-r).... in S
Then in S f(x+a)=(x+a-r)...
so the splitting ffield of f(x+a) is a subset of S. ssimilarly the reverse inclusion. hence etc.