Which statement about the zeros of the polynomial (x - 1)(x + 1)(x - 3)(x + 2) is true?

Which statement about the zeros of the polynomial (x - 1)(x + 1)(x - 3)(x + 2) is true?

• A. The zeros are -2, -1, 1, and 3.
• B. The zeros are -2 and 1 only.
• C. The zeros are -1 and 2 only.
• D. The zeros are 0, 0, 0, 0.

Answer: (A)

Zeros of a polynomial written as a product come from setting each factor to zero. For (x − 1)(x + 1)(x − 3)(x + 2), each linear factor gives a root: x − 1 = 0 gives x = 1; x + 1 = 0 gives x = −1; x − 3 = 0 gives x = 3; x + 2 = 0 gives x = −2. So the zeros are −2, −1, 1, and 3. This matches the option listing all four roots. The other descriptions would miss some zeros or claim a value that doesn’t make the polynomial zero (for example, x = 0 gives a nonzero product).

Zeros of a polynomial written as a product come from setting each factor to zero. For (x − 1)(x + 1)(x − 3)(x + 2), each linear factor gives a root: x − 1 = 0 gives x = 1; x + 1 = 0 gives x = −1; x − 3 = 0 gives x = 3; x + 2 = 0 gives x = −2. So the zeros are −2, −1, 1, and 3. This matches the option listing all four roots. The other descriptions would miss some zeros or claim a value that doesn’t make the polynomial zero (for example, x = 0 gives a nonzero product).