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

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

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

First, we write x - 1 as the divisor and x^3 - 3x^2 + 3x - 1 as the dividend:

x^2 - 2x + 1
x - 1 | x^3 - 3x^2 + 3x - 1

Next, we divide x into x^3 to get x^2, and write that above the dividend. We then multiply x - 1 by x^2 to get x^3 - x^2, and write that below the dividend. We subtract to get -2x^2 + 3x - 1:

x^2 - 2x + 1
x - 1 | x^3 - 3x^2 + 3x - 1
x^3 - x^2
----------
-2x^2 + 3x - 1

We then repeat the process with -2x^2, dividing x into -2x^2 to get -2x, and writing that above the dividend. We multiply x - 1 by -2x to get -2x^2 + 2x, and write that below the dividend. We subtract to get x - 1:

x^2 - 2x + 1
x - 1 | x^3 - 3x^2 + 3x - 1
x^3 - x^2
----------
-2x^2 + 3x - 1
-2x^2 + 2x
----------
x - 1

Since the degree of the remainder x - 1 is less than the degree of the divisor x - 1, we have found the remainder. Therefore, the remainder when x^3 - 3x^2 + 3x - 1 is divided by x - 1 is 0.