Question

Find the least common multiple of x^{3}-x^{2}+x-1 and x^{2}-1. Write the answer in factored form.

Factors and multiples
ANSWERED
asked 2020-11-12
Find the least common multiple of \(x^{3}-x^{2}+x-1\ and\ x^{2}-1\). Write the answer in factored form.

Answers (1)

2020-11-13
Factor the given polynomials:
\(x^{3}-x^{2}+x-1=x^{2}(x-1)+(x-1)\)
\(=x(-1)(x^{2}+1)\)
\(x^{2}-1=(x(-1)(x+1)\)
The lowest common multiple is the product of all the factors of each polynomial to the highest degree. Each of the factors \(x-1\), and \(x^{2}+1\) all have a degree of 1 so the lowest common multiple is \((x-1)(x+1)(x^2+1)\).
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