[tex]\displaystyle\\
(x^2-x)(x^2-x-22)+40=\\
=x^4-x^3-x^3+x^2-22x^2+22x+40=\\
=x^4-2x^3-21x^2+22x+40=\\
=x^4-2x^3-21x^2+22x+40=~~~~~~~\Big|~22x = 42x - 20x\\
=x^4-2x^3-21x^2+42x -20x+40=\\
=x^3(x-2)-21x(x-2) -20(x-2)=\\
=(x-2)( x^3-21x -20)=\\
=(x-2)( x^3+0x^2-21x -20)=~~~~~~~\Big|~0x^2 = -5x^2+5x^2\\
=(x-2)( x^3-5x^2+5x^2-21x -20)=~~~~~~~\Big|~-21x=-25x+4x\\
=(x-2)( x^3-5x^2+5x^2-25x+4x -20)=\\
=(x-2)( x^2(x-5)+5x(x-5)+4(x -5))=\\
=(x-2)(x-5)( x^2+5x+4)=\\
=(x-2)(x-5)( x^2+5x+4)=~~~~~~~\Big|~5x=x+4x
[/tex]
[tex]\displaystyle\\
=(x-2)(x-5)( x^2+x+4x+4)=\\
=(x-2)(x-5)( x(x+1)+4(x+1))=\\
=\boxed{\bf (x-2)(x-5)(x+1)( x+4)}
[/tex]
