If $x^{4} + x^{3} - 2 x^{2} + x + 1$ is divided by $x - 1$ then remainder = .

x - 1

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x^{2} - 3

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Solution

The correct option is D 2
Dividing $x^{4} + x^{3} - 2 x^{2} + x + 1$ by $x - 1$ :

$\begin{matrix} x^{3} + 2 x^{2} + 1 x - 1 x^{4} + x^{3} - 2 x^{2} + x + 1 x^{4} - x^{3} - -------------- - 2 x^{3} - 2 x^{2} + x + 1 2 x^{3} - 2 x^{2} ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ x + 1 x - 1 - ---- - 2 \end{matrix}$

Hence, remainder = 2.

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When $x^{4} + x^{3} - 2 x^{2} + x + 1$ is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).

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