\(\Rightarrow\left(x^2+2x+4\right)-x\left(x+1\right)⋮x+1\)
\(\Rightarrow\left(x^2+2x+4\right)-\left(x^2+x\right)⋮x+1\)
\(\Rightarrow x^2+2x+4-x^2-x⋮x+1\)
\(\Rightarrow x+4⋮x+1\)
\(\Rightarrow\left(x+4\right)-\left(x+1\right)⋮x+1\)
\(\Rightarrow x+4-x-1⋮x+1\)
\(\Rightarrow3⋮x+1\)
\(\Rightarrow x+1\inƯ\left(3\right)=\left(1;-1;3;-3\right)\)
Ta có bảng sau :
x + 1 1 -1 3 -3
x 0 -2 2 -4
Mà \(x\in Z\)
\(\Rightarrow x\in\left(0;-2;2;-4\right)\)
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