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x³ + 7x² - x - 7
Factor x² out of the first two terms and -1 out of the last two terms:
x²(x + 7) - 1(x + 7)
Factor (x + 7) of of the two terms:
(x + 7)(x² - 1)
Factor the second parentheses as the difference of two squares:
(x + 7)(x - 1)(x + 1)
Edwin