Solve (x - 1)(x + 2)(x - 3) = 0. Which set contains all roots?

Solve (x - 1)(x + 2)(x - 3) = 0. Which set contains all roots?

• A. { -2, 1, 3 }
• B. { -3, 0, 2 }
• C. { -2, 2, 4 }
• D. { -1, 1, 3 }

Answer: (A)

When a product equals zero, at least one factor must be zero. So set each factor to zero and solve: x − 1 = 0 → x = 1 x + 2 = 0 → x = −2 x − 3 = 0 → x = 3 The roots are −2, 1, and 3. The set that contains all of these numbers is {−2, 1, 3}. Any other option would miss one of these roots or include a number that isn’t a root, so it wouldn’t capture all solutions.

When a product equals zero, at least one factor must be zero. So set each factor to zero and solve:

x − 1 = 0 → x = 1

x + 2 = 0 → x = −2

x − 3 = 0 → x = 3

The roots are −2, 1, and 3. The set that contains all of these numbers is {−2, 1, 3}. Any other option would miss one of these roots or include a number that isn’t a root, so it wouldn’t capture all solutions.