Question:
When $p(x)=x^{3}-a x^{2}+x$ is divided by $(x-a)$, the remainder is
(a) 0
(b) $a$
(c) $2 a$
(d) $3 a$
Solution:
By remainder theorem, when $p(x)=x^{3}-a x^{2}+x$ is divided by $(x-a)$, then the remainder $=p(a)$.
Putting $x=a$ in $p(x)$, we get
$p(a)=a^{3}-a \times a^{2}+a=a^{3}-a^{3}+a=a$
$\therefore$ Remainder $=a$
Hence, the correct answer is option (b).