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      Question

      Factor the polynomial: x³ - 6x² + 11x -

      6.
      A (x - 1)(x - 2)(x - 3) Correct Answer Incorrect Answer
      B (x + 1)(x + 2)(x + 3) Correct Answer Incorrect Answer
      C (x - 2)(x - 3)(x - 1) Correct Answer Incorrect Answer
      D (x - 1)(x + 2)(x - 3) Correct Answer Incorrect Answer

      Solution

      Using synthetic division to find roots, we test possible rational roots. Testing x = 1: 1³ - 6(1)² + 11(1) - 6 = 0. Thus, (x - 1) is a factor. Dividing x³ - 6x² + 11x - 6 by (x - 1): The result is x² - 5x + 6 = (x - 2)(x - 3). So, the complete factorization is (x - 1)(x - 2)(x - 3). Correct Answer: a) (x - 1)(x - 2)(x - 3).

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