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

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Solution

So answer is $x + 2$
$x^{4} + x^{3} - 2 x^{2} + x + 1 = (x - 1) (x^{3} + 2 x^{2}) + (x + 1)$

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