Factor x^2 - 5x + 6.

Factor x^2 - 5x + 6.

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

Answer: (A)

When factoring a quadratic with a leading coefficient of 1, you look for two numbers that multiply to the constant term and add to the coefficient of x. Here, the constant term is 6 and the coefficient of x is -5, so you want two numbers that multiply to 6 and add to -5. Those numbers are -2 and -3 because (-2) × (-3) = 6 and (-2) + (-3) = -5. So the factorization is (x - 2)(x - 3). Expanding confirms it: x^2 - 3x - 2x + 6 = x^2 - 5x + 6. Other pairings don’t match both the middle term and the constant: for example, (x - 1)(x - 6) gives x^2 - 7x + 6, (x - 3)(x - 4) gives x^2 - 7x + 12, and (x - 2)(x - 4) gives x^2 - 6x + 8.

When factoring a quadratic with a leading coefficient of 1, you look for two numbers that multiply to the constant term and add to the coefficient of x. Here, the constant term is 6 and the coefficient of x is -5, so you want two numbers that multiply to 6 and add to -5. Those numbers are -2 and -3 because (-2) × (-3) = 6 and (-2) + (-3) = -5.

So the factorization is (x - 2)(x - 3). Expanding confirms it: x^2 - 3x - 2x + 6 = x^2 - 5x + 6. Other pairings don’t match both the middle term and the constant: for example, (x - 1)(x - 6) gives x^2 - 7x + 6, (x - 3)(x - 4) gives x^2 - 7x + 12, and (x - 2)(x - 4) gives x^2 - 6x + 8.