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

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x^{2} + x + 1

x^{2} + x - 1

- x^{2} - x - 1

x^{2} + 1

answer is D.

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Detailed Solution

$x^{3} + x^{2} + x + 1$

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

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

$f (x) = g (x) q (x) + r (x)$

$= (x + 1) (x^{2} + 1) + 0$

$\Rightarrow q (x) = x^{2} + 1$

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