To find a linear factor of the polynomial \( x^3 - 5x^2 + 6x \), we first factor the expression completely.
We can start by factoring out the greatest common factor (GCF), which is \( x \):
\[ x^3 - 5x^2 + 6x = x(x^2 - 5x + 6) \]
Now, we need to factor the quadratic \( x^2 - 5x + 6 \). We look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 meet this criterion.
Therefore, we can factor the quadratic as:
\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]
Putting this together, we have:
\[ x^3 - 5x^2 + 6x = x(x - 2)(x - 3) \]
Now, the complete factorization of the polynomial is:
\[ x(x - 2)(x - 3) \]
The linear factors are \( x \), \( x - 2 \), and \( x - 3 \).
Given that \( x \) is one of the linear factors, the other correct factors are \( x - 2 \) and \( x - 3 \). Among the provided choices, the factor:
- \( x - 2 \)
is indeed one of the factors of the polynomial \( x^3 - 5x^2 + 6x \).
So the correct response is:
x - 2