Phân tích đa thức thành nhân tử: `2(x²-6x+1 )+ 5(x²-6x+1)(x²+1) + 2(x²+1)²`

Đáp án:

Đề ở phần cmt:

`2.(x^2-6x+1)^2+5.(x^2-6x+1).(x^2+1)+2.(x^2+1)^2`

`=2.(x^2-6x+1)^2+(x^2-6x+1).(x^2+1)+4.(x^2-6x+1).(x^2+1)+2.(x^2+1)^2`

`=[2.(x^2-6x+1)^2+(x^2-6x+1).(x^2+1)]+[4.(x^2-6x+1).(x^2+1)+2.(x^2+1)^2]`

`=(x^2-6x+1).[2.(x^2-6x+1)+(x^2+1)]+2.(x^2+1).[2.(x^2-6x+1)+(x^2+1)]`

`=[(x^2-6x+1)+2.(x^2+1)].[2.(x^2-6x+1)+(x^2+1)]`

`=(x^2-6x+1+2x^2+2).(2x^2-12x+2+x^2+1)`

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

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

`=9.(x^2-2x+1).(x^2-4x+1)`

`=9.(x-1).(x-1).(x^2-4x+1)`