`a,x^7 + x^2 + 1`
`=x^7 + x^6 + x^5 - x^6 - x^5 - x^4+ x^4 + x^3 + x^2 - x^3 - x^2 - x + x^2 + x + 1`
`=x^5(x^2 + x + 1) - x^4(x^2 + x + 1) + x^2(x^2 + x + 1) - x(x^2 + x + 1) + (x^2 + x + 1)`
`=(x^5 - x^4 + x^2 - x + 1)(x^2 + x + 1)`
`b,(x^2-2x)(x^2-2x-1)-6`
$\text{Đặt: $x^2$ - 2x = y}$
$\text{⇒ $x^2$ - 2x - 1 = y - 1}$
$\text{Thay vào biểu thức, ta có:}$
`⇒ y(y - 1) - 6 = y^2 - y - 6`
`= y^2 - 3y + 2y - 6 = y(y - 3) + 2(y - 3)`
`= (y-3)(y+2)`
$\text{Quay trở lại, ta có:}$
`⇒ (x^2 - 2x - 3)(x^2 - 2x + 2)`
`c, (x^2+4x-3)^2-5x(x^2+4x-3)+6x^2`
$\text{Đặt: x^2 + 4x - 3 = y}$
$\text{Thay vào biểu thức, ta có:}$
`⇒y^2 - 5xy + 6x^2=y^2-3xy-2xy+6x^2`
`=y(y-3x)-2x(y-3x)=(y-2x)(y-3x)`
$\text{Quay trở lại, ta có:}$
`⇒(x^2+4x-3-2x)(x^2+4x-3-3x)`
`=(x^2-2x-3)(x^2+x-3)`
