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put this solution on YOUR website! Find the least common multiple of x³ - x² - x + 1 and x² - 1. Write the answer in factored form.
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
