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
x^3-x^2+x-1
=(x-1)(x^2+1)
x^2-1
=(x-1)(x+1)
So, the least common multiple is (x-1)(x+1)(x^2+1)
