P(x) = x³ +2x² -x -2الجذور الممكنة = {1, -1, 2, -2}* P(1) = 0 → x1 = 1* P(-1) = 0 → x2 = -1* P(2) = 12 → 2 ليس جذرا لكثيرة الحدودوباقي (x³ +2x² -x -2)/(x-2) هو 12* P(-2) = 0 → x3 = -2P(x) = x³ +2x² -x -2الجذور الممكنة = {1, -1, 2, -2}* P(1) = 0 → x1 = 1→ x³ +2x² -x -2 = (x-1)(x² +3x +2)هنا, r1=-1 وQ(x) = x² +3x +2* Q(-1) = 0 → x2 = -1→ x³ +2x² -x -2 = (x-1)(x² +3x +2) = (x-1)(x+1)(x+2)Having used the ""p"/"q"" result above (or, to be fair, any other means) to find all the real rational roots of a particular polynomial, it is but a trivial step further to partially factor that polynomial using those roots.