` 1) ` ` x^5 - x^4 + x^3 - x^2 `
` = (x^5 - x^4) + (x^3 - x^2) `
` = x^4 (x - 1) + x^2 (x - 1) `
` = (x - 1)(x^4 + x^2) `
` = x^2 (x - 1)(x^2 + 1) `
` 2) ` ` x^3 - 2x^2 - x^2 - x `
` = x(x^2 - 2x - x - 1) `
` = x(x^2 - 3x - 1) `
` 3) ` ` -x^2 - 2xy - y^2 + 3x + 3y `
` = -(x^2 + 2xy + y^2) + (3x + 3y) `
` = -(x + y)^2 + 3(x + y) `
` = (x + y)(3 - x - y) `
` 4) ` ` ac^2 - ad - bc^2 + cd + bd - c^3 `
` = (ac^2 - bc^2 - c^3) - (ad - bd - cd) `
` = c^2 (a - b - c) - d(a - b - c) `
` = (a - b - c)(c^2 - d) `