[tex]\displaystyle \\
(x+1) ~\texttt{este divizor al lui }~(x^2+5)~~\texttt{este echivalent cu:}\\\\
\frac{x^2+5}{x+1} \in N \\\\
\texttt{Rezolvare: } \\\\
\frac{x^2+5}{x+1}=\frac{x^2-1+6}{x+1}=\frac{x^2-1}{x+1} + \frac{6}{x+1} = x-1 + \frac{6}{x+1} \\\\
D_6 =\{ 1;~2;~3;~6\} \\\\
x+1 = 1~~ \Longrightarrow~~ x=0 \\\\
x+1 = 2~~ \Longrightarrow~~ x=1 \\\\
x+1 = 3~~ \Longrightarrow~~ x=2 \\\\
x+1 = 6~~ \Longrightarrow~~ x=5 \\\\
\texttt{Raspuns: }~~~\boxed{x\in \{0;~1;~2;~6\}}[/tex]
