Question

Find the remainder when $x^3-3x^2+4x-5$ is divided by (x - 2).

Answer 1

Here $f\left(x\right)=x^3=3x^2+4x-5$

When a function $f\left(x\right)$ is divided by $x+a$, then the remainder is given by $f(-a)$:

So, in this case remainder will be $f\left(2\right)$:
$f\left(2\right)=(2{)}^3-3(2{)}^2+4\left(2\right)-5$

$=-1$