One of the factor of `x^(3) -x^(2) + x -1` is ____

Answer

To find one of the factors of the polynomial \( x^3 - x^2 + x - 1 \), we can use the Factor Theorem. The Factor Theorem states that if \( f(a) = 0 \) for a polynomial \( f(x) \), then \( x - a \) is a factor of that polynomial.

### Step-by-Step Solution:

1. **Identify the Polynomial**:
We have the polynomial \( f(x) = x^3 - x^2 + x - 1 \).

2. **Assume a Potential Factor**:
We will check if \( x - 1 \) is a factor. This means we will evaluate \( f(1) \).

3. **Substitute \( x = 1 \) into the Polynomial**:
\[ f(1) = (1)^3 - (1)^2 + (1) - 1 \]
\[ = 1 - 1 + 1 - 1 \]
\[ = 0 \]

4. **Conclusion**:
Since \( f(1) = 0 \), by the Factor Theorem, \( x - 1 \) is indeed a factor of the polynomial \( x^3 - x^2 + x - 1 \).

### Final Answer:
One of the factors of \( x^3 - x^2 + x - 1 \) is \( x - 1 \).

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