Question

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

• A. $a$
• B. $3a$
• C. $5a$
• D. $7a$

Answer 1

Answer: (A), (C)

Correct option is C.$5a$

According to the Remainder Theorem, if $p\left(x\right)$ is divided by $(x-b)$ then the remainder obtained can be calculated as $p\left(a\right)$.

Here, $p\left(x\right)=x^3-a{x}^2+6x-a$, and the zero of $x-a$ is $a$

So, $p\left(a\right)=a^3-a\times a^2+6\times a-a$

$=a^3-a^3+5a$

$=5a$

$\therefore 5a$ is the remainder when $x^3-a{x}^2+6x-a$ is divided by $x-a$.