Phân tích các đa thức sau thành nhân tử

Đáp án+Giải thích các bước giải:

 `a)`

`(x+2)^{3}+1`

`=(x+2)^{3}+1^{3}`

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

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

`=(x+3).(x^{2}+3x+3)`

`b)`

`x^{3}+6x^{2}+12x+9`

`=(x^{3}+6x^{2}+12x+8)+1`

`=(x^{3}+3.x^{2}.2+3.x.2^{2}+2^{3})+1`

`=(x+1)^{3}+1^{3}`

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

`=(x+2).(x^{2}+2x+1-x-1+1)`

`=(x+2).(x^{2}+x+1)`

`c)`

`x^{3}+6x^{2}+12x+7`

`=(x^{3}+6x^{2}+12x+8)-1`

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

`=(x+2)^{3}-1^{3}`

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

`=(x+1).(x^{2}+4x+4+x+2+1)`

`=(x+1).(x^{2}+5x+7)`

`d)`

`2x^{3}+6x^{2}+12x+8`

`=x^{3}+(x^{3}+6x^{2}+12x+8)`

`=x^{3}+(x^{3}+3.x^{2}.2+3.x.2^{2}+2^{3})`

`=x^{3}+(x+2)^{2}`

`=(x+x+2).[x^{2}-x.(x+2)+(x+2)^{2}]`

`=(2x+2).(x^{2}-x^{2}-2x+x^{2}+4x+4)`

`=2.(x+1).(x^{2}+2x+4)`