To find a factor of the polynomial \( x^3 - 5x^2 + 6x \), we can first factor out the common term:
\[ x^3 - 5x^2 + 6x = x(x^2 - 5x + 6) \]
Next, we need to factor the quadratic \( x^2 - 5x + 6 \). We can look for two numbers that multiply to \( 6 \) (the constant term) and add up to \( -5 \) (the coefficient of the linear term).
The factors of \( 6 \) that add to \( -5 \) are \( -2 \) and \( -3 \):
\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]
Now, substituting back, we have:
\[ x^3 - 5x^2 + 6x = x(x - 2)(x - 3) \]
So, the complete factorization of the polynomial is:
\[ x(x - 2)(x - 3) \]
Given that \( x \) itself is a factor, and we are looking for another linear factor among the options provided, we see that \( x - 2 \) is indeed a factor.
Among the choices provided:
- \( x + 3 \)
- \( x + 2 \)
- \( x^2 + 5x + 9 \)
- \( x - 2 \)
The correct answer is:
\[ \boxed{x - 2} \]