If the polynomial $x^{3} - x^{2} + x - 1$ is divided by $x - 1$ , then the quotient is :

x^{2} - 1

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x^{2} + 1

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x^{2} - x + 1

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x^{2} + x + 1

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Solution

The correct option is B $x^{2} + 1$
Divide $x^{3} - x^{2} + x - 1$ by $x - 1$

$x - 1$ $¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯) x^{3} - x^{2} + x - 1 ($ $x^{2} + 1$
$- (x^{3} - x^{2})$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ + x - 1$
$- (x - 1)$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 0$

Hence, $B$ is correct.

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