The remainder when $x^4-x^3+x^2-2x+1$ is divided by $x-2$ is:

If $p\left(x\right)$ is any polynomial of degree higher than or equal to one, and "$a$" is any real number, the remainder theorem holds. If you divide $p\left(x\right)$ by the linear polynomial $x-a$, the result is $p\left(a\right)$.

To find the value of remainder, we have to find the value of $p\left(2\right).$

Here, $p\left(x\right)$ = $x^4-x^3+x^2-2x+1$, and the zero of $x-2$ is $2$.

          $p\left(2\right)$ = ${\left(2\right)}^4-{\left(2\right)}^3+{\left(2\right)}^2-2\left(2\right)+1$

                   =17

So, by the Remainder Theorem, $17$ is the remainder when is $x^4-x^3+x^2-2x+1$ divided by $x-2$.