Factor x^2 - 5x + 6.

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

Answer: (C)

Factoring a quadratic like x^2 - 5x + 6 means finding two numbers a and b that add to the coefficient of x and multiply to the constant term. Here, you want a + b = 5 and ab = 6. The pair that fits is 2 and 3, since 2 + 3 = 5 and 2·3 = 6. This lets you write the expression as (x - 2)(x - 3). Expanding confirms the result: x^2 - 3x - 2x + 6 equals x^2 - 5x + 6. Other factor pairs of 6 don’t give the required sum of 5 in this form, so they don’t factor this quadratic correctly.