\(2x^2+3x+2⋮x+2\)
\(\Rightarrow2x^2+4x-x+2⋮x+2\)
\(\Rightarrow2x\left(x+2\right)-\left(x-2\right)⋮x+2\)
Vì \(2x\left(x+2\right)⋮\left(x+2\right)\) . Để \(2x\left(x+2\right)- \left(x-2\right)⋮x+2\Leftrightarrow\left(x-2\right)⋮x+2\)
\(\Leftrightarrow\left(x+2\right)-4⋮x+2\Rightarrow4⋮x+2\)
\(\Rightarrow x+2\inƯ\left(4\right)=\left\{1;2;4;-1;-2;-4\right\}\)
| x+2 | 1 | 2 | 4 | -1 | -2 | -4 |
| x | -1 | 0 | 2 | -3 | -4 | -6 |
Vậy \(x\in\left\{-1,0,2,-3,-4,-6\right\}\)
