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

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

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

`= 3x^4 + 3x^2 + 3 - x^4 - 2x^3 - 3x^2 - 2x - 1 `

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

`= 2x^4 - 2x^3 - 2x + 2`

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

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

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

`= 2(x - 1)(x^3 - 1) `

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

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