Question
What is the highest common factor of (x³ - x² - x -
15) and (x³ - 3x² - 3x + 9)?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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