[tex]\displaystyle\\
a)\\
x^4-x^2- 2x + 2 =\\
=x^2(x^2-1)-2(x-1)=\\
=x^2(x+1)(x-1)-2(x-1)=\\
=(x-1)[x^2(x+1)-2]=\\
=(x-1)[x^3+x^2-2]=\\
=(x-1)[x^3+x^2-1-1]=\\
=(x-1)[x^3-1+x^2-1]=\\
=(x-1)[(x-1)(x^2+x+1)+(x-1)(x+1)]=\\
=(x-1)(x-1)(x^2+x+1+x+1)=\\
=\boxed{(x-1)^2(x^2+2x+2)}[/tex]
[tex]\displaystyle\\
b)\\
x^2y + xy^2+x^3y - xy^3=\\
=xy[(x + y)+(x^2-y^2)]=\\
=xy[(x + y)+(x+y)(x-y)]=\\
=\boxed{xy(x + y)(1+x-y)}
[/tex]
