Factor x^2 - 5x + 6.

Factor x^2 - 5x + 6.

• A. (x-1)(x-6)
• B. (x-2)(x-3)
• C. (x+2)(x-3)
• D. (x-3)(x-4)

Answer: (B)

When you factor a quadratic with leading coefficient 1, you look for two numbers that multiply to the constant term and add to the coefficient of x. For x^2 - 5x + 6, you want two numbers that multiply to 6 and sum to -5. The numbers -2 and -3 fit perfectly, since (-2) + (-3) = -5 and (-2)(-3) = 6. This lets you write x^2 - 5x + 6 as (x - 2)(x - 3). Expanding confirms the result: (x - 2)(x - 3) = x^2 - 5x + 6. The other factor pairs don’t match both the sum and the product required, so they don't reproduce the original expression.

When you factor a quadratic with leading coefficient 1, you look for two numbers that multiply to the constant term and add to the coefficient of x. For x^2 - 5x + 6, you want two numbers that multiply to 6 and sum to -5. The numbers -2 and -3 fit perfectly, since (-2) + (-3) = -5 and (-2)(-3) = 6. This lets you write x^2 - 5x + 6 as (x - 2)(x - 3). Expanding confirms the result: (x - 2)(x - 3) = x^2 - 5x + 6. The other factor pairs don’t match both the sum and the product required, so they don't reproduce the original expression.