Factor and solve: x^2 - 5x + 6 = 0.

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

Answer: (C)

When you factor a quadratic of the form x^2 + bx + c, you look for two numbers that multiply to c and add to b. Here c is 6 and b is -5, so you want two numbers that multiply to 6 and add to -5. Those numbers are -2 and -3. This lets you factor the quadratic as (x - 2)(x - 3) = 0. By the zero-product property, either x - 2 = 0 or x - 3 = 0, giving x = 2 or x = 3. So the solutions are x = 2 or x = 3.

Other values listed don’t satisfy the equation: for example, substituting -2, 1, 6, or -3 into x^2 - 5x + 6 does not yield zero, so they aren’t solutions.