Question

n^3+2n-n^2-2 chia hết n-1 với n thuộc Z

Answer 1

\(n^3+2n-n^2-2=n^2\left(n-1\right)+2\left(n-1\right)=\left(n-1\right)\left(n^2+2\right)⋮\left(n-1\right)\forall n\in Z\)

Answer 2

\(n^3-n^2+2n-2\)

\(=n^2\left(n-1\right)+2\left(n-1\right)\)

\(=\left(n-1\right)\left(n^2+2\right)⋮n-1\)