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

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Solution

We have $x^{3} - a x^{2} + 6 x - a$
Apply remainder theorem
$x - a = 0$
$x = a$
Put $x = a$ in equation.
$(a)^{3} - a (a)^{2} + 6 a - a$
$= a^{3} - a^{3} + 6 a - a$
$= 6 a - a$
$= 5 a$
Then reminder is $5 a$

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