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

Question

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

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Answer

$\text { Let } p(x)=x^3-a x^2+6 x-a$
$x-a=0$
$\Rightarrow x=a$
$\therefore \text { Remainder }=(a)^3-a(a)^2+6(a)-a$
$=a^3-a^3+6 a-a$
$=5 a$

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