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    Question

    What is the highest common factor of (x³ - x² - x -

    15) and (x³ - 3x² - 3x + 9)?
    A (x - 1) Correct Answer Incorrect Answer
    B (x - 2) Correct Answer Incorrect Answer
    C (x - 3) Correct Answer Incorrect Answer
    D (x - 5) Correct Answer Incorrect Answer

    Solution

    x³ - x² - x - 15 = x³ - 3x² + 2x² - 6x + 5x - 15 = x²(x - 3) + 2x(x - 3) + 5(x - 3) = (x - 3)(x² + 2x + 5) x³ - 3x² - 3x + 9 = x²(x - 3) - 3(x - 3) = (x - 3)(x² - 3) ∴ HCF = (x - 3)

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