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

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Solution

$p (x) = x^{3} - a x^{2} + 6 x - a$
When p(x) is divided by x - a, the remainder is p(a).
Substitute x = a in p(x).
$p (a) = a^{3} - a^{3} + 6 a - a = 5 a$

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