What's the remainder when $x^{3} - a x^{2} + 6 x - a$ is divided by x - a.

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Solution

Given that, $p (x) = x^{3} - a x^{2} + 6 x - a$

We know that,
When p(x) is divided by x - a, the remainder is p(a).

Now, substitute x = a in $p (x)$
$p (a) = a^{3} - a^{3} + 6 a - a = 5 a$

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