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

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Solution

By remainder theorem, the required remainder is equal to $p (1)$
$p (x) = x^{3} - 4 x^{2} + 3 x + 1$
$∴ p (1) = 1^{3} - 4 (1)^{2} + 3 (1) + 1 = 1 - 4 + 3 + 1 = 1$
$∴$ the required remainder $= p (1) = 1$

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