How can the quadratic equation x² - 5x + 6 be factored?

The quadratic equation x² - 5x + 6 can be factored by finding two numbers that multiply to the constant term, which is 6, and add up to the coefficient of the x term, which is -5.

In this case, the two numbers that meet these criteria are -2 and -3. When you multiply these two numbers (-2 and -3), you get 6 (the constant term). When you add them, you have -2 + (-3) = -5, which matches the coefficient of the x term.

Thus, the equation can be factored as (x - 2)(x - 3).

This factorization means that the roots of the equation, or where the equation equals zero, are at x = 2 and x = 3. Therefore, the correct choice accurately represents this factorization method for the given quadratic equation.