\(n^3+n+2=n^3+n^2-n^2+1+n+1\)
\(=n^2\left(n+1\right)-\left(n-1\right)\left(n+1\right)+n+1\)
\(=\left(n+1\right)\left(n^2-n+2\right)\)
Do \(n\in N\)*\(\Rightarrow n\ge1\Rightarrow\left\{{}\begin{matrix}n+1\ge2\\n^2-n+2\ge2\end{matrix}\right.\)
\(\Rightarrow\left(n+1\right)\left(n^2-n+2\right)\) có ít nhất 3 ước số \(\Rightarrow\) là hợp số