Question

phân tích các đa thức sau thanh nhân tử:

D = x^3 - 6x^2 + 2x - 8

E = 4x^3 - 13x^2 + 9x - 18

F = 2x^4 - 21x^3 - 30x^2 - 105x +50

Answer 1

`#3107.101107`

`D = x^3 - 6x^2 + 12x - 8?`

`= x^3 - 3 * x^2 * 2 + 3 * x * 2^2 - 2^3`

`= (x - 2)^3`

`E = 4x^3 - 13x^2 + 9x - 18`

`= 4x^3 - x^2 - 12x^2 + 9x - 18`

`= 4x^3 - x^2 - 12x^2 + 3x + 6x - 18`

`= (4x^3 - x^2 + 6x) - (12x^2 - 3x + 18)`

`= x(4x^2 - x + 6) - 3(4x^2 - x + 6)`

`= (x - 3)(4x^2 - x + 6)`

`F = 2x^4 - 21x^3 - 30x^2 - 105x +50`

`= 2x^4 - 25x^3 + 4x^3 - 50x^2 + 20x^2 + 20x - 125x + 50`

`= (2x^4 - 25x^3 + 10x^2) + (4x^3 - 50x^2 + 20x) + (10x^2 - 125x + 50)`

`= x^2(2x^2 - 25x + 10) + 2x(2x^2 - 25x + 10) + 5(2x^2 - 25x + 10)`

`= (x^2 + 2x + 5)(2x^2 - 25x + 10)`