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

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

• A. (x - 3)(x - 2)
• B. (x - 1)(x - 6)
• C. (x + 5)(x - 1)
• D. (x + 3)(x + 2)

Answer: (A)

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

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