Factor completely: x^2 - 5x + 6.

Factor completely: x^2 - 5x + 6.

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

Answer: (A)

Factoring quadratics of this form relies on 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, so we need two numbers that multiply to 6 and add to 5. The pairs that multiply to 6 are 1 and 6 (sum 7) and 2 and 3 (sum 5). Since the middle term is negative, we take -2 and -3. That gives x^2 - 5x + 6 = (x - 2)(x - 3). Expanding confirms the result: x^2 - 3x - 2x + 6 = x^2 - 5x + 6. The other options either multiply to the wrong constant, produce the wrong sign for the middle term, or give a different midterm altogether, so they don’t match the original expression.

Factoring quadratics of this form relies on 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, so we need two numbers that multiply to 6 and add to 5. The pairs that multiply to 6 are 1 and 6 (sum 7) and 2 and 3 (sum 5). Since the middle term is negative, we take -2 and -3. That gives x^2 - 5x + 6 = (x - 2)(x - 3). Expanding confirms the result: x^2 - 3x - 2x + 6 = x^2 - 5x + 6. The other options either multiply to the wrong constant, produce the wrong sign for the middle term, or give a different midterm altogether, so they don’t match the original expression.