To find a factor of the polynomial \( x^3 - 5x^2 + 6x \), we can start by factoring out the greatest common factor (GCF) from the expression.
The polynomial can be rewritten as:
\[ x(x^2 - 5x + 6) \]
Next, we can factor the quadratic expression \( x^2 - 5x + 6 \). We look for two numbers that multiply to \( 6 \) (the constant term) and add to \( -5 \) (the coefficient of \( x \)). The numbers \( -2 \) and \( -3 \) satisfy these conditions:
\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]
Now we can express the original polynomial as:
\[ x(x - 2)(x - 3) \]
The linear factors of the polynomial are \( x \), \( x - 2 \), and \( x - 3 \).
The response options given are \( x + 2 \), \( x + 3 \), \( x^2 + 5x + 6 \), and \( x - 2 \).
Among these, \( x - 2 \) is a correct factor of the original polynomial \( x^3 - 5x^2 + 6x \).
Thus, another correct factor is:
\( x - 2 \)