Question

When $x^3-6x^2+12x-4$ is divided by $x-2$, the remainder is

• A. $4$
• B. $0$
• C. $5$
• D. $6$

Answer 1

The correct option is A $4$

Let $p\left(x\right)=$ $x^3-6x^2+12x-4$
and $g\left(x\right)=$ $x-2$
$x-2=0$
$\Rightarrow x=2$
To find remainder, when $p\left(x\right)$ when by $g\left(x\right)$
By using remainder theorem, remainder is $p\left(2\right)$
thus, $p\left(2\right)=(2{)}^3-6(2{)}^2+12\left(2\right)-4$
$=8-24+24-4$
$=4$