To find a factor of the polynomial \( x^3 - 5x^2 + 6x \), we can first factor out the common term, which is \( x \):
\[ x^3 - 5x^2 + 6x = x(x^2 - 5x + 6) \]
Next, we need to factor the quadratic polynomial \( x^2 - 5x + 6 \). We can look for two numbers that multiply to 6 (the constant term) and add to -5 (the coefficient of x). These two numbers are -2 and -3.
Therefore, we can factor \( x^2 - 5x + 6 \) as:
\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]
Putting it all together, we have:
\[ x^3 - 5x^2 + 6x = x(x - 2)(x - 3) \]
The factors of \( x^3 - 5x^2 + 6x \) are \( x \), \( x - 2 \), and \( x - 3 \).
From the options provided, we can conclude that \( x - 2 \) is another correct factor of the polynomial.