Find the least common multiple of x³ – x² + x – 1 and x² – 1 . Write the answer in factored form.
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OpenStudy (luigi0210):
Factor both and what do you get?
OpenStudy (anonymous):
(x - 1)(x - 1)(x + 1) and (x - 1)(x + 1)?
OpenStudy (anonymous):
(x - 1)(x - 1)(x + 1) and (x - 1)(x + 1)?
OpenStudy (anonymous):
Can I just like say the answer?
OpenStudy (anonymous):
Do you know how to solve it shelby?
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OpenStudy (luigi0210):
Close.. it would actually be:
\[\LARGE (x^2+1)(x-1)~and~(x+1)(x-1)\]
OpenStudy (anonymous):
(x + 1)(x – 1)(x² + 1)
OpenStudy (anonymous):
How did you get that @Anonymouseee
OpenStudy (anonymous):
x^3 - x^2 + x - 1 = (x - 1)(x^2 + 1) That is the big key to the problem and that was done using synthetic division. x^2 - 1 = (x - 1)(x + 1) So, you take (x - 1)(x^2 + 1) from the first, but you only have to take "x + 1" from the second because you already have a "x - 1" factor from the first. And that's it!
OpenStudy (luigi0210):
Yea, factor an x^2 and 1..
\[\LARGE x^2(x-1)+1(x-1)\]
\[\LARGE (x^2+1)(x-1)\]
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