When p(x) = x3 – ax2

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).

 

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