=x^11-x^2+x^2+x+1

=x^2(x^9-1)+(x^2+x+1)

=x^2[(x^3)^3-1^3)+(x^2+x+1)

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

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

Đặt nhân tử chung là x^2+x+1 rồi phá hết ngoặc là xong
 

`b) x^2+8xy+16y^2+2x+8y-3`

`= x^ 2 + 2. x .4 y + ( 4 y )^ 2 + 2 ( x + 4 y ) − 3`

`= ( x + 4 y ) ^2 + 2 ( x + 4 y ) + 1 − 2^ 2`

`= ( x + 4 y + 1 )^ 2 − 2^ 2`

`= ( x + 4 y + 1 − 2 ) ( x + 4 y + 1 + 2 )`

`= ( x + 4 y − 1 ) ( x + 4 y + 3 )`
c,(x^2 - x +1)^2   - 5x(x^2 - x + 1) +4x^2
-Đặt t=(x^2−x+1)t=(x^2−x+1)

(x^2−x+1)^2−5x(x^2−x+1)+4x^2(x^2−x+1)^2−5x(x^2−x+1)+4x^2

=t^2−5xt+4x^2
=t^2−5xt+4x^2

=t^2−4xt−xt+4x^2=t^2−4xt−xt+4x^2

=t(t−4x)−x(t−4x)=t(t−4x)−x(t−4x)

=(t−4x)(t−x)=(t−4x)(t−x)

=(x^2−x+1−4x)(x^2−x+1−x)=(x^2−x+1−4x)(x^2−x+1−x)

=(x^2−5x+1)(x^2−2x+1)=(x^2−5x+1)(x^2−2x+1)

=(x^2−5x+1)(x−1)^2