What is remainder when $x^{3} - 2 x^{2} + x + 1$ is divided by $(x - 1)$ ?

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Solution

The correct option is C 1
Let's divide $x^{3} - 2 x^{2} + x + 1$ by $x - 1$
$x - 1$ $¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯) x^{3} - 2 x^{2} + x + 1 ($ $x^{2} - x$
$- (x^{3} - x^{2})$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - x^{2} + x + 1$
$- (- x^{2} + x)$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 1$
Hence, the remainder is $1$ .

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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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