Which of the following represents the factored form of the quadratic equation \(x^2 - 5x + 6\)?

To determine the factored form of the quadratic equation (x^2 - 5x + 6), we begin by identifying the numbers that multiply to the constant term (6) and add up to the coefficient of the linear term (-5).

In this case, we are seeking two numbers that when multiplied together give us (6) and when added together yield (-5). The pair of numbers that satisfy both of these conditions is (-2) and (-3). This is because:

• ((-2) \times (-3) = 6)

• ((-2) + (-3) = -5)

Using these two numbers, we can express the quadratic in its factored form as ((x - 2)(x - 3)). Note how the factors correspond directly to the roots of the equation: if (x) is equal to (2) or (3), the original equation will yield zero, confirming they are the correct factors.

When we compare this factorization to the provided answer choices, the form ((x - 3)(x - 2)) matches the correct factorization of the quadratic. This shows that the expression