From the factorization (x-2)(x-3) = 0, what are the solutions for x?

From the factorization (x-2)(x-3) = 0, what are the solutions for x?

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

Answer: (B)

Whenever a product equals zero, one of the factors must be zero. Here, the equation (x-2)(x-3) = 0 means either x-2 = 0 or x-3 = 0. Solving those gives x = 2 or x = 3. These values make one factor vanish, so the product becomes zero. Any other number won’t make either factor zero, so it won’t satisfy the equation. Therefore, the solutions are x = 2 and x = 3.

Whenever a product equals zero, one of the factors must be zero. Here, the equation (x-2)(x-3) = 0 means either x-2 = 0 or x-3 = 0. Solving those gives x = 2 or x = 3. These values make one factor vanish, so the product becomes zero. Any other number won’t make either factor zero, so it won’t satisfy the equation. Therefore, the solutions are x = 2 and x = 3.