Your answer is:
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Post question's edit:
You want to prove that the polynomial is reducible in $\Bbb Z[x]$. By (the second) Gauss's lemma, if it is reducible in $\Bbb Q[x]$, then it also is in $\Bbb Z[x]$. Since its degree is $3$, it is reducible (over $\Bbb Q$) if, and only if, there is a rational root. Now note that in case Eistein's criterion doesn't work, you still won't know wether it is reducible or not, so that shouldn't be the way to go. You want to find a rational root. Try finding roots using the rational root theorem.
Something else you can try is to factor your polynomial. If you can't do this, you can always put the polynomial as input in a very well known on-line software.
Best Answer
If it were reducible in $\mathbb Q[X,Y]$ then you could substitute $X$ for $Y$ and you'd have a factorisation of $X^n-13X^4$, hence of $X^{n-4}-13$, which is impossible. (Some powers of $X$ will need borrowing if $n<4$, and if $n=4$ it's clear.)