To find a factor of the polynomial \( x^3 - 5x^2 + 6x \), we can first factor out the common term \( x \):
\[ x^3 - 5x^2 + 6x = x(x^2 - 5x + 6) \]
Next, we need to factor the quadratic \( x^2 - 5x + 6 \). To do this, we look for two numbers that multiply to 6 and add up to -5. The two numbers that fit this criterion are -2 and -3. Thus, we can factor the quadratic as follows:
\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]
Putting it all together, we have:
\[ x^3 - 5x^2 + 6x = x(x - 2)(x - 3) \]
The linear factors of \( x^3 - 5x^2 + 6x \) are \( x \), \( x - 2 \), and \( x - 3 \).
Since the question asks for another correct factor, and \( x \) is already provided as a factor, the correct responses from the options given would be:
- \( x - 2 \)
- \( x - 3 \), if it was listed as an option (which it is not).
Therefore, the correct response from the provided options is:
x - 2.