\(2n^2+3n+2⋮n+1\\ \Leftrightarrow2n\left(n+1\right)+\left(n+1\right)+1⋮n+1\\ Vì\left\{{}\begin{matrix}2n\left(n+1\right)⋮n+1\\n+1⋮n+1\end{matrix}\right.\\ \Rightarrow1⋮n+1\\ \Rightarrow n+1\inƯ_{\left(1\right)}\\ \Rightarrow n+1\in\left\{1;-1\right\}\\ \Leftrightarrow n\in\left\{0;-2\right\}\\ Vậy.....\)