Solve x^2 - 9 = 0.

• A. -3 or -9
• B. 0 or 9
• C. 1 or -1
• D. 3 or -3

Answer: (D)

Think of this as a difference of squares. x^2 - 9 factors as (x - 3)(x + 3). For the product to be zero, one of the factors must be zero, so x - 3 = 0 or x + 3 = 0, giving x = 3 or x = -3. These two values make x^2 equal to 9, so they satisfy the equation. Any other number won’t make x^2 equal 9, so it won’t solve the equation.