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

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Solution

Concept: 1 Mark
Application: 1 Mark

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

According to remainder theorem, remainder is equal to p(a) when p(x) is divided by $(x - a)$
$p (a) = a^{3} - a a^{2} + 6 a - a$ $= a^{3} - a^{3} + 5 a = 5 a$

Therefore, remainder is equal to $5 a$ when $p (x) = x^{3} - a x^{2} + 6 x - a$ is divided by $(x - a)$ .

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