To factor the expression \( x^3 - 5x^2 + 6x \), we can start by factoring out the greatest common factor, which is \( x \):
\[ x^3 - 5x^2 + 6x = x(x^2 - 5x + 6) \]
Next, we need to factor the quadratic \( x^2 - 5x + 6 \). We are looking for two numbers that multiply to \( 6 \) (the constant term) and add to \( -5 \) (the coefficient of \( x \)). These numbers are \( -2 \) and \( -3 \).
Thus, we can factor the quadratic as:
\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]
Now, substituting this back into the expression, we get:
\[ x(x^2 - 5x + 6) = x(x - 2)(x - 3) \]
Therefore, the complete factorization of \( x^3 - 5x^2 + 6x \) is:
\[ x(x - 2)(x - 3) \]
Since \( x \) is given to be one of the factors, the remaining factors are \( (x - 2) \) and \( (x - 3) \).
Thus, another correct factor is either \( (x - 2) \) or \( (x - 3) \).