\(x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)
1) \(x^2-y^2-5x+5y\)
=\(\left(x+y\right)\left(x-y\right)-5\left(x+y\right)\)
=\(\left(x+y\right)\left(x-y-5\right)\)
2) \(x^3-3x^2-3x+1\)
=\(x^3+x^2-4x^2-4x+x+1\)
=\(x^2\left(x+1\right)-4x\left(x+1\right)+\left(x+1\right)\)
=\(\left(x^2-4x+1\right)\left(x+1\right)\)
=\(\left(x-\left(2+\sqrt{3}\right)\right).\left(x-\left(2-\sqrt{3}\right)\right).\left(x+1\right)\)
3) \(3x^2-7x-10\)
=\(3x^2+3x-10x-10\)
=\(3x\left(x+1\right)-10\left(x+1\right)\)
=\(\left(3x-10\right)\left(x+1\right)\)
4) \(x^2-3x+2\)
=\(x^2-2x-x+2\)
=\(x\left(x-2\right)-\left(x-2\right)\)
=\(\left(x-1\right)\left(x-2\right)\)
