`x^4 + 6x^3 - 11x^2 + 6x + 1`

`= x^4 + 6x^3 + 9x^2 - 20x^2 + 6x + 1`

`= (x^2 + 3x)^2 - 20x^2 + 6x + 1`

`= (x^2+3x+1)^2 - 2(x^2+3x) - 1 - 20x^2 + 6x + 1`

`= (x^2+3x+1)^2 - 2x^2 - 6x - 20x^2 + 6x`

`= (x^2+3x+1)^2 - 22x^2`

`= (x^2+3x+1)^2 - (sqrt(22)x)^2`

`= (x^2 + 3x + 1 - sqrt(22)x)(x^2 + 3x + 1 + sqrt(22)x)`

`= [x^2 + (3 - sqrt(22))x + 1][x^2 + (3 + sqrt(22))x + 1]`