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

• A. x=2 or x=3
• B. x=1 or x=4
• C. x=0 or x=6
• D. x=-2 or x=-3

Answer: (A)

When you solve a quadratic by factoring, you look for two numbers that multiply to the constant term and add to the coefficient of x. For x^2 - 5x + 6, the numbers are -2 and -3, so it factors as (x - 2)(x - 3). By the zero-product property, set each factor to zero: x - 2 = 0 or x - 3 = 0, giving x = 2 or x = 3. These values make the left side zero, so they satisfy the equation. Other suggested values don’t satisfy it (for example, x = 1 gives 1 - 5 + 6 = 2, not 0).