Question

What is the remainder of x3 − 2x2 + 2x + k divided by (x − 1)?

Answer 1

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

`x^3-2x^2+2x+k^{}`

divided by x-1 is:

`1^3-2\cdot1^2+2\cdot1+k\text{.}`

Simplifying the above expression we get:

`\begin{gathered} 1-2+2+k, \\ 1+k. \end{gathered}`

Answer: First option.