Factor x³ - x² - x + 1 

Factor x² out of the first two terms:

x²(x - 1) - x + 1

Factor -1 out of the last two terms:

x²(x - 1) - 1(x - 1)

Factor (x - 1) out

(x - 1)(x² - 1)

Factor (x² - 1) as the difference of squares:

(x - 1)(x - 1)(x + 1)

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Factor x² - 1 as the difference of squares

(x - 1)(x + 1)

Both those factors are contained in (x - 1)(x - 1)(x + 1)

therefore (x - 1)(x - 1)(x + 1) is the least common multiple, and

it can be written as (x - 1)²(x + 1)

Edwin