Given the expression:
[tex]x^{2}-xy-3x+2+2y[/tex]We will factor the expression as follows:
[tex]\begin{gathered} x^{2}-xy-3x+2+2y \\ =(x^2-3x+2)+(-xy+2y) \\ =(x-2)\cdot(x-1)-y(x-2) \\ =(x-2)\cdot(x-y-1) \end{gathered}[/tex]so, the answer will be:
[tex](x-2)(x-y-1)[/tex]