Let $P(n)$ be an irreducible polynomial of degree $2$ over the positive integers. Show that there exist infinitely many positive integers $n$ such that $P(n)$ divides $n!$.

Edit: motivation by examples: A) $p(n)=n^2+1$ (true)
B) $p(n)=n^2+n+1$

Let $P(n)$ be an irreducible polynomial of degree $2$ over the positive integers. Do there exist infinitely many positive integers $n$ such that $P(n)$ divides $n!$?

Edit: motivation by examples: A) $p(n)=n^2+1$ (true, $21^2+1$ divides $21!$).
B) $p(n)=n^2+n+1$ (true, $74^2+74+1$ divides $74!$).

Let be $P(n)$ a polynomial of degree $2$ irreducible in positive integers. Exist infinitely  $n$ such that $P(n)$ divide $n!$.

Edit: motivation by examples A)$p(n)=n^2+1$(true)
B)$p(n)=n^2+n+1$

Let $P(n)$ be an irreducible polynomial of degree $2$ over the positive integers. Show that there exist infinitely many positive integers $n$ such that $P(n)$ divides $n!$.

Edit: motivation by examples: A)  $p(n)=n^2+1$  (true)
B)  $p(n)=n^2+n+1$

Let be $P(n)$ a polynomial of degree $2$ irreducible in positive integers. Exist infinitely $n$ such that $P(n)$ divide $n!$.

Let be $P(n)$ a polynomial of degree $2$ irreducible in positive integers. Exist infinitely $n$ such that $P(n)$ divide $n!$.

Edit: motivation by examples A)$p(n)=n^2+1$(true)
B)$p(n)=n^2+n+1$