Question

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)

Answer 1

Hello,
Answer B


`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)\\`

Answer 2

Option B is correct.

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.