Để \(\left(2n^3-7n^2-8n+9\right)⋮\left(n-2\right)\)
\(\Leftrightarrow\left[\left(n-2\right).\left(2n^2-3n-14\right)+19\right]⋮\left(n-2\right)\)
Mà \(\left[\left(n-2\right).\left(2n^2-3n-14\right)\right]⋮\left(n-2\right)\)
\(\Leftrightarrow19⋮\left(n-2\right)\)
\(\Leftrightarrow\left(n-2\right)\inƯ\left(19\right)\)
\(\Leftrightarrow\left(n-2\right)\in\left\{1;19;-1;-19\right\}\)
\(\Leftrightarrow n\in\left\{3;21;1;-17\right\}\)
Vậy : \(n\in\left\{3;21;1;-17\right\}\) thì \(A⋮\left(n-2\right)\)
