find the least common multiple of: x^3-x^2+x-1 and x^2-1?

NetherCraft 0

answer choices: 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)

2 Answers

  • First, factor the polynomials:

    x^3-x^2+x-1 = x^2(x-1) + (x-1), using grouping.

    = (x^2 + 1)(x -1).

    x^2 -1 = (x – 1)(x + 1).

    Finally, the LCM is the product of the list of factors, using commons factors between polynomials once each:

    So, LCM = (x^2 + 1)(x – 1)(x + 1), choice b.

  • b





    So, the least common multiple is (x-1)(x+1)(x^2+1)

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