Calculate the remainder when x^3 - 2x + 1 is divided by x - 1.

The remainder when x^3 - 2x + 1 is divided by x - 1 is 0.

To find the remainder when x^3 - 2x + 1 is divided by x - 1, we can use polynomial long division.

First, we write x - 1 as a factor of x^3 - 2x + 1 by dividing x^3 by x, which gives us x^2. We then multiply x - 1 by x^2 to get x^3 - x^2. We subtract this from x^3 - 2x + 1 to get -x^2 - 2x + 1.

Next, we write x - 1 as a factor of -x^2 - 2x + 1 by dividing -x^2 by x, which gives us -x. We then multiply x - 1 by -x to get -x^2 + x. We subtract this from -x^2 - 2x + 1 to get -3x + 1.

Finally, we write x - 1 as a factor of -3x + 1 by dividing -3x by x, which gives us -3. We then multiply x - 1 by -3 to get -3x + 3. We subtract this from -3x + 1 to get 2.

Since the degree of the remainder, 2, is less than the degree of the divisor, x - 1, the remainder is simply the constant term, which is 2. Therefore, the remainder when x^3 - 2x + 1 is divided by x - 1 is 2.