Question

Tìm \(n\)∈\(Z\)

\(n^2+2n-5\) chia hết cho \(n+2\)

Answer 1

\(n^2+2n-5⋮n+2\)

=>\(n\left(n+2\right)-5⋮n+2\)

=>\(n+2\in\left\{1;-1;5;-5\right\}\)

=>\(n\in\left\{-1;-3;3;-7\right\}\)

Answer 2

Ta có:

n² + 2n - 5

= n(n + 2) - 5

Để (n² + 2n - 5) ⋮ (n - 2) thì 5 ⋮ (n - 2)

⇒ n - 2 ∈ Ư(5) = {-5; -1; 1; 5}

⇒ n ∈ {-3; 1; 3; 7}