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The LCM of \( \Large x^{3}-1 \), \( \Large x^{2}-1 \) and \( \Large \left(x-1\right)^{2} \) is
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A) \( \Large \left(x+1\right) \left(x-1\right) \left(x^{2}+x+1\right) \) |
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B) \( \Large \left(x+1\right)^{2} \left(x-1\right) \left(x^{2}-x+1\right) \) |
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C) \( \Large \left(x-1\right)^{2} \left(x-1\right) \left(x^{2}+x+1\right) \) |
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D) \( \Large \left(x-1\right)^{2} \left(x+1\right) \left(x^{2}-x+1\right) \) |
Correct Answer:
| C) \( \Large \left(x-1\right)^{2} \left(x-1\right) \left(x^{2}+x+1\right) \) |
Description for Correct answer:
\( \Large \left(x^{3}-1\right)= \left(x-1\right) \left(x^{2}+x+1\right) \)
\( \Large x^{2}-1 = \left(x+1\right) \left(x-1\right) \)
\( \Large \left(x-1\right)^{2} = \left(x-1\right) \left(x-1\right) \)
LCM \( \Large \left(x-1\right)^{2} \left(x+1\right) \left(x^{2}+x+1\right) \)
\( \Large \left(x^{3}-1\right)= \left(x-1\right) \left(x^{2}+x+1\right) \)
\( \Large x^{2}-1 = \left(x+1\right) \left(x-1\right) \)
\( \Large \left(x-1\right)^{2} = \left(x-1\right) \left(x-1\right) \)
LCM \( \Large \left(x-1\right)^{2} \left(x+1\right) \left(x^{2}+x+1\right) \)
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