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`\color{red}{a,}`

`M = (x^3 - 2x^2 + 3x + 3)/(x - 1)` `(x \ne 1)`

`M = (x^3 - x^2 - x^2  + x + 2x - 2 + 4)/(x - 1)`

`M = (x^2.(x - 1) - x.(x - 1) + 2.(x - 1) + 4)/(x - 1)`

`M = ((x - 1).(x^2  - x + 2) + 4)/(x - 1)`

`M = x^2 - x + 2 + 4/(x - 1)`

Để `M in ZZ`

`<=> 4/(x - 1) in ZZ`

`<=> x - 1 in Ư_{(4)} = {-1;1;-2;2;-4;4}`

`<=> x in {0;2;-1;3;-3;5}` `(tm)`

Vậy `M in ZZ <=> x in {0;2;-1;3;-3;5}` 

$\\$

`N = (2x^3 - 5x^2 + 8x + 8)/(2x - 1)` `(x \ne 1/2)`

`N = (2x^3 - x^2 - 4x^2 + 2x + 4x - 2 + 10)/(2x - 1)`

`N = [x^2.(2x - 1) - 2x.(2x - 1) + 2.(2x - 1) + 10]/[2x - 1]`

`N = [(2x - 1).(x^2 - 2x+ 2) + 10]/[2x - 1]`

`N = x^2 - 2x + 2 + 10/(2x - 1)`

Để `N in ZZ`

`<=> 10/(2x - 1) in ZZ`

`<=> 2x - 1 in Ư_{(10)} = {-1;1;-2;2;-5;5;-10;10}`

mà: `2x - 1` lẻ

`=> 2x - 1 in {-1;1;-5;5}`

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

`<=> x in {0;1;-2;3}` `(tm)`

Vậy `N in ZZ <=> x in {0;1;-2;3}`

`#Eirlys07`