To solve this question we will use the remainder theorem:
Remainder Theorem: If a polynomial f(x) is divided by x−a, then the remainder is the constant f(a).
Therefore, by the Remainder Theorem, we get that the remainder of
[tex]x^3-2x^2+2x+k^{}[/tex]
divided by x-1 is:
[tex]1^3-2\cdot1^2+2\cdot1+k\text{.}[/tex]
Simplifying the above expression we get:
[tex]\begin{gathered} 1-2+2+k, \\ 1+k. \end{gathered}[/tex]
Answer: First option.
