An expression, which when divided by $(x + 1)$ gives $(x^{2} - x + 1)$ as quotient and $3$ as remainder is equal to:

x^{3} - 2

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x^{3} - 1

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x^{3} + 2

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(x^{3} + 4)

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Solution

The correct option is D $(x^{3} + 4)$
Dividend=Divisor $\times$ Quotient $+$ Remainder
$\Rightarrow (x + 1) \times (x^{2} - x + 1) + 3$
$\Rightarrow x (x^{2} - x + 1) + (x^{2} - x + 1) + 3$
$\Rightarrow (x^{3} - x^{2} + x + x^{2} - x + 1 + 3)$
$\Rightarrow (x^{3} + 4)$

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