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Find the least common multiple of x3 - x2 + x - 1 and x2 - 1. Write the answer in factored form. A. (x + 1)2(x - 1) B. (x + 1)(x - 1)(x2 + 1) C. (x3 - x2 + x - 1)(x2 - 1) D. (x + 1)(x - 1)(x2 - 1)

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caylus
Hello,
Answer B

[tex]x^3-x^2+x-1=(x-1)(x^2+1)\\ x^2-1=(x+1)(x-1)\\ lcm=(x-1)(x+1)(x^2+1)\\ [/tex]

Answer:

Option B is correct.

Step-by-step explanation:

Given Expression , x³ - x² + x - 1   and x² - 1

We have to find Least common multiple of both expression then answer it in factor form.

First we factorize individual expressions.

Consider,

x³ - x² + x - 1

= x² ( x - 1 ) + 1 ( x - 1 )

= ( x² + 1 ) ( x - 1 )

Now consider,

x² - 1

= ( x - 1 )( x + 1 )

Common factor = ( x - 1 )

So, LCM = ( x - 1 ) ( x + 1 )( x² + 1 )

Therefore, Option B is correct.

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