Đáp án:+Giải thích các bước giải:

`a, (2x^3 + 5x^2 - 2x + 12) : (2x^2 - x + 1)`

`= (2x^3 - x^2 + x + 6x^2 - 3x + 3 + 9) : (2x^2 - x + 1)`

`= [x(2x^2 - x + 1) + 3(2x^2 - x + 1) + 9] : (2x^2 - x + 1)`

`= [(2x^2 - x + 1)(x + 3) + 9] : (2x^2 - x + 1)`

`= x + 3` dư `9`

`b, (2x^3 - 5x^2 + 6x - 15) : (2x - 5)`

`= [(2x^3 - 5x^2) + (6x - 15)] : (2x - 5)`

`= [x^2 (2x - 5) + 3(2x - 5)] : (2x - 5)`

`= (2x - 5)(x^2 + 3) : (2x - 5)`

`= x^2 + 3`

`c, (x^4 - x - 12) : (x - 2)`

`= (x^4 - 2x^3 + 2x^3 - 4x^2 + 4x^2 - 8x + 7x - 14 + 2) : (x - 2)`

`= [x^3 (x - 2) + 2x^2 (x - 2) + 4x(x - 2) + 7(x - 2) + 2] : (x - 2)`

`= [(x - 2)(x^3 + 2x^2 + 4x + 7) + 2] : (x -2 )`

`= x^3 + 2x^2 + 4x + 7` dư `2`