For p(x) = x³ − 2x² − 5x + 6, which is the smallest positive zero of p(x)?

Correct answer: 1

The correct answer is A, 1. A zero is a value r for which p(r) = 0. Factor the polynomial: x³ − 2x² − 5x + 6 = (x − 1)(x − 3)(x + 2). Therefore the zeros are 1, 3 and −2. The positive zeros are 1 and 3, and the smallest positive one is 1. Option A is correct. Option B is not a zero because p(2) = 8 − 8 − 10 + 6 = −4. Option C is a zero, since p(3) = 27 − 18 − 15 + 6 = 0, but it is not the smallest positive zero. Option D gives p(4) = 64 − 32 − 20 + 6 = 18, so it is not a zero. The phrase ‘smallest positive’ is important; without it, both 1 and 3 would be correct and the question would be ambiguous.