Show that a polynomial f(x) over a field k is irreducible if and only if the polynomial f(x + 1) is irreducible.

Question

I am very much unsure what definitions and formulas are relevant for this question. I've toyed around with the lemma "An element a ∈ R is a root of a polynomial f ∈ R[x] if and only if (x − a) divides f" but come up with nothing useful.

Answer 1

Hint: If $f(x+1)=g(x)h(x)$ then $f(x)=g(x-1)h(x-1)$.