Find the remainder when $x^{4} + x^{3} - 2 x^{2} + x + 1$ is divided by $x - 1$

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Solution

The correct option is A $2$
Given polynomial $p (x)$ is $x^{4} + x^{3} - 2 x^{2} + x + 1$

When $p (x)$ is divided by $(x - 1),$ the remainder is $p (1)$
$= 1^{4} + 1^{3} - 2 \times 1 + 1 + 1$ (By remainder theorem)
$= 1 + 1 - 2 + 1 + 1$
$= 2$

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