Find the remainder when $x^{3} - p x^{2} + 6 x - p$ is divided by $x - p$

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Solution

Given polynomial $x^{3} - p x^{2} + 6 x - p$ divided by $x - p$
If divided by $x - p$ then $x - p = 0$ or $x = p$
Replace x by p we get
$q (x) = x^{3} - p x^{2} + 6 x - p$
$q (p) = (p)^{3} - p (p)^{2} + 6 (p) - p$
$\Rightarrow q (p) = p^{3} - p^{3} + 6 p - p$
$\Rightarrow q (p) = 5 p$

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