Phân tích đa thức thành nhân tử : `6)` `2x^4 -9x^3 +14x^2 -9x+2` `7)a(x^2 +1)-x(a^2 +1)` `8)(x+y+z)^2 -x^2 -y^2 +z^2`

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`2x^4 - 9x^3 + 14x^2 - 9x + 2`

`= (2x^4 - 4x^3) - (5x^3 - 10x^2) + (4x^2 - 8x) - (x - 2)`

`= 2x^3 (x-2) - 5x^2 (x-2) + 4x (x-2) - (x-2)`

`= (x - 2) (2x^3 - 5x^2 + 4x - 1)`

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

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

`= (x - 2) (2x - 1) (x^2 - 2x + 1)`

`= (x-2) (2x-1) (x-1)^2`

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`a (x^2 + 1) - x (a^2 + 1)`

`= ax^2 + a - a^2 x - x`

`= (ax^2 - a^2 x) + (a - x)`

`= ax (x - a) - (x - a)`

`= (x - a) (ax - 1)`

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`(x+y+z)^2 - x^2 - y^2 + z^2`

`= [(x+y) + z]^2 - x^2 - y^2 + z^2`

`= (x + y)^2 + 2 . (x + y) . z + z^2 - x^2 - y^2 + z^2`

`= x^2 + 2xy + y^2 + 2zx + 2yz + z^2 - x^2 - y^2 + z^2`

`= 2z^2 + 2xy + 2yz + 2zx`

`= 2 (z^2 + xy + yz + zx)`

`= 2 [(z^2 + zx) + (yz + xy)]`

`= 2 [z (z + x) + y (z+x)]`

`= 2 (z+x) (z+y)`