X³-3x²-8x+24=0

Solve x^3 − 3x^2 − 8x + 24 = 0.

• Try rational roots (±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24).
  f(3) = 27 − 27 − 24 + 24 = 0, so x = 3 is a root.

• Divide by (x − 3) (synthetic division with 3):
  x^3 − 3x^2 − 8x + 24 ÷ (x − 3) → quotient x^2 − 8.

• Factor the quadratic: x^2 − 8 = 0 → x = ±√8 = ±2√2.

Solutions: x = 3, x = 2√2, x = −2√2.