Factor the quadratic x^2 + 5x + 6.

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

Answer: (B)

When a quadratic has a leading coefficient of 1, you can factor it by finding two numbers that multiply to the constant term and add to the middle coefficient. Here, the constant term is 6 and the middle coefficient is 5. Look at factor pairs of 6: 1 and 6 (sum 7) and 2 and 3 (sum 5). The pair that adds to 5 is 2 and 3, so the quadratic factors as (x+2)(x+3). Expanding confirms: (x+2)(x+3) = x^2 + 5x + 6. Other factor pairs would produce different middle terms, so they don’t match this polynomial.