What is the HCF of (x³ + 3x² - x - 3) and (x³ + 4x² + x - 6)?
(x³ + 3x² - x - 3) = x² (x + 3) - 1 (x + 3) = (x + 3) (x² - 1) x³ + 4x² + x - 6 = x³ + 3x² + x² + 3x - 2x - 6 = x² (x + 3) + x (x + 3) - 2 (x + 3) = (x + 3) (x² + x - 2) ∴ HCF = (x + 3)
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