Question

Cho đa thức M(x)=\(x^2-2;N\left(x\right)=-x^3-x\)

Tìm \(x\in Z\) để \(\dfrac{N\left(x\right)}{M\left(x\right)}\in Z\)

Answer 1

\(\Leftrightarrow-x^3-x⋮x^2-2\)

\(\Leftrightarrow-x^3+2x-3x⋮x^2-2\)

\(\Leftrightarrow-3x^2⋮x^2-2\)

\(\Leftrightarrow x^2-2\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

hay \(x\in\left\{1;-1;2;-2\right\}\)