Question

Using remainder theorem, find the reminder when $x^3-a{x}^2+2x-a$ is divided by $x-a$.

• A. $a$
• B. $a+2$
• C. $a+1$
• D. $a-2$

Answer 1

The correct option is A $a$

Let $p\left(x\right)=a^3+a{x}^2+2x-a$ and
$g\left(x\right)=x-a$
The remainder when $p\left(x\right)$ is divided by $g\left(x\right)=x-a$ is $p\left(a\right)$ (By Remainder Theorem)
$p\left(a\right)=a^3-a(a{)}^2+2(a)-a$
$=a^3-a^3+2a-a$
$=a$
Therefore,
Remainder=$a$