Question

Find the least common multiple of x 3 - x 2 + x - 1 and x 2 - 1. write the answer in factored form.

a. (x + 1) 2(x - 1)
b. (x + 1)(x - 1)(x 2 + 1)
c. (x 3 - x 2 + x - 1)(x 2 - 1)
d. (x + 1)(x - 1)(x 2 - 1)

Answer 1

B.(x+1)(x-1)(x2+1)

Explanation:

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Answer 2

Let
f(x) = x³ - x² + x - 1
g(x) = x² - 1

By the remainder theorem, f(1) = 1 -1 + 1 - 1 = 0
Therefore (x-1) is a factor.
Perform synthetic division.

1 | 1 -1 1 -1
1 0 1
--------------
1 0 1 0

Therefore,
f(x) = (x-1)(x²+1)

Also,
g(x) = (x+1)(x-1)

Answer: b.
The least common multiple for f(x) and g(x) is (x + 1)(x - 1)(x² + 1).