`a)`
`x^8 + x^4 + 1`
`= (x^8 + 2x^4 + 1) - x^4`
` = [ (x^4)^2 + 2 . x^4 . 1 + 1^2] - (x^2)^2`
` = (x^4 + 1)^2 - (x^2)^2`
` = (x^4 + 1 + x^2)(x^4 + 1 - x^2)`
` = (x^4 + 2x^2 + 1 - x^2)(x^4 - x^2 + 1)`
` = [ (x^2)^2 + 2 . x^2 . 1 + 1^2 - x^2] (x^4 - x^2 +1)`
` = [ (x^2 +1)^2 - x^2] (x^4 - x^2 +1)`
`= (x^2 + 1 - x)(x^2 + 1 +x)(x^4 - x^2 + 1)`
`b)`
Đặt `A = (x^2 - 2x)^3 - 3x^2 + 6x + 2`
`= (x^2 - 2x)^3 - 3(x^2 - 2x) + 2`
Đặt `x^2 - 2x = t`
Khi đó ta có :
`A = t^3 - 3t + 2`
` = (t^3 - 2t^2 + t) + (2t^2 - 4t + 2)`
` = t (t^2 - 2t + 1) + 2 (t^2 - 2t+1)`
`= (t+2)(t^2-2t+1)`
` = (t+2)(t-1)^2`
Mà `t = x^2-2x` nên
`A = (x^2 -2x+2)(x^2 - 2x- 1)^2`
