Solve x³-2x²-5x+6=0

x³ - 2x² - 5x + 6 = 0

x³ - x² - x² + x - 6x + 6 = 0

x² (x - 1) - x (x - 1) - 6 (x - 1) = 0

(x - 1) (x² - x - 6) = 0

(x - 1) (x² + 2x - 3x - 6) = 0

(x - 1) [x (x + 2) - 3 (x + 2) ] = 0

(x - 1) (x + 2) (x - 3) = 0

x - 1 = 0 = > x₁ = 1

x + 2 = 0 = > x₂ = - 2

x - 3 = 0 = > x₃ = 3