Q: Show (x - 2) is a factor of x^3 - 3x^2 - 6x + 8, then factor fully. Step 1: P(2) = 8 - 12 - 12 + 8 = -8. Not 0! So (x - 2) is NOT a factor. Try x = 1: 1 - 3 - 6 + 8 = 0. So (x - 1) is a factor. Step 2: Divide: (x^3 - 3x^2 - 6x + 8) / (x - 1) = x^2 - 2x - 8. Step 3: x^2 - 2x - 8 = (x - 4)(x + 2). Answer: (x - 1)(x - 4)(x + 2).