Question

Tìm x thuộc Z để x^2 + x + 5 chia hết cho x+1

 

Answer 1

\(x^2+x+5\) chia hết x+1

\(x.\left(x+1\right)+5\) chia hết x+1

5 chia hết x+1

Suy ra \(x+1\inƯ\left(5\right)\)

\(x+1\in\left\{-5;-1;1;5\right\}\)

\(x\in\left\{-6;-2;0;4\right\}\)

Answer 2

`x^2 + x + 5 vdots x + 1`

`=> x(x+1) + 5 vdots x + 1`

Vì `x(x+1) vdots x + 1` nên `5 vdots x + 1`

`=> x + 1 in Ư(5) = {-5;-1;1;5}`

`=> x in {-6;-2;0;4}`

Vậy `x in {-6;-2;0;4}`