Cubic equations ax³ + bx² + cx + d = 0 have degree 3 with up to 3 real roots. Solving methods: (1) Rational root theorem: Test divisors of d/a; (2) Factor theorem: If f(r) = 0, then (x-r) is factor; (3) Synthetic division: Divide by (x-r) to reduce to quadratic. Example: x³ - 6x² + 11x - 6 = 0. Test x=1: 1 - 6 + 11 - 6 = 0 (root). Factor out (x-1): x³ - 6x² + 11x - 6 = (x-1)(x² - 5x + 6) = (x-1)(x-2)(x-3). Roots: 1, 2, 3. Vieta's formulas: Sum of roots = -b/a; sum of products of pairs = c/a; product = -d/a. Exam tip: Rational root test saves time (test small integers first). Always verify one root before factoring.