AP Precalculus – Polynomial Functions and Complex Zeros – Drill 4

About This Drill

AP Precalculus – Polynomial Functions and Complex Zeros – Drill 4 is a Math practice drill covering Polynomial Functions and Complex Zeros. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Master the most heavily tested Unit 1 topic on the AP® Precalculus exam: polynomial zeros, sign analysis, factoring, and the complex conjugate pairs theorem. This drill covers AP® Topic 1.5 with question styles drawn directly from official exam questions, including sign chart analysis, factoring to count real zeros, and applying the conjugate pairs theorem to degree-4 polynomials.

Questions in This Drill

1. Let p(x) = −x(x − 4)(x + 2). On which of the following intervals is p(x) ≥ 0?
2. Let p(x) = x(x − 3)(x + 1)(x − 5). How many of the intervals in the partition of the real number line formed by the zeros of p contain points where p(x) < 0?
3. Let p(x) = (x + 3)(x² − 2x − 15). How many distinct real zeros does p have?
4. A polynomial function p has real coefficients and degree 4. It is known that 2 + 3i is a zero of p, and that p has exactly two distinct real zeros. Which of the following must be true?
5. A polynomial function p has degree 3, real coefficients, and leading coefficient 1. The zeros of p are x = 2, x = −1, and x = 4. What is p(0)?