Solve x^2 - 5x + 6 = 0.

• A. x = 1 or x = 6
• B. x = -2 or x = -3
• C. x = 2 or x = 3
• D. x = 0 or x = 5

Answer: (C)

Factoring a quadratic and using the zero-product property is the idea here. The expression x^2 - 5x + 6 factors as (x - 2)(x - 3) because the numbers -2 and -3 multiply to 6 and add to -5. Setting the product to zero gives x - 2 = 0 or x - 3 = 0, so x = 2 or x = 3. Substituting confirms they work: 2^2 - 5(2) + 6 = 0 and 3^2 - 5(3) + 6 = 0. Other values don’t satisfy the equation, since they don’t make the expression equal to zero.