Show that if $a_{0}+a_{1}x+...+a_{n}x^{n}$ is irreducible in K[X] then $a_{n}+a_{n-1}x+...+a_{0}x^{n}$ is also irreducible.

Question

Let K be a field and let $$ f(x) = a_{0}+a_{1}x+...+a_{n}x^{n} $$ is irreducible in K[X] then $$ a_{n}+a_{n-1}x+...+a_{0}x^{n} $$ is also irreducible.

Answer 1

If $P$ denotes the first polynomial, then the second is $Q(X) = X^n P(X^{-1})$. Try to use this.