Question

n^2+3*n+4 chia hết cho n+3

Answer 1

Ta có :

\(n^2+3n+4⋮n+3\)

Mà \(n+3⋮n+3\)

\(\Leftrightarrow\left\{{}\begin{matrix}n^2+3n+4⋮n+3\\n^2+3n⋮n+3\end{matrix}\right.\)

\(\Leftrightarrow4⋮n+3\)

Vì \(n\in N;4⋮n+3\Leftrightarrow n+3\inƯ\left(4\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}n+3=1\\n+3=2\\n+3=4\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=-2\left(loại\right)\\n=-1\left(loại\right)\\n=1\end{matrix}\right.\)

Vậy ..........