Divide:
$x^{3} - 3 x^{2} + 3 x - 1$ by $x - 1$

(x^{2} - 2 x + 1)

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(x^{2} - x + 1)

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(x^{2} - 2 x + 9)

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(x^{2} + 2 x + 1)

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Solution

The correct option is A $(x^{2} - 2 x + 1)$
$= \frac{x^{3} - 3 x^{2} + 3 x - 1}{(x - 1)} = \frac{x^{3} - 3 x^{2} \times 1 - 3 x \times 1^{2} - 1^{3}}{(x - 1)} = \frac{{(x - 1)}^{3}}{(x - 1)} = {(x - 1)}^{2} = x^{2} - 2 x + 1$

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