Complex Zeros, Polynomial Construction, and Descartes’ Rule of Signs | Precalculus 5.5.c

This is Part 3 of a three-part lesson covering Precalculus 5.5: Zeros of Polynomial Functions. In this video, you will learn how to construct a polynomial from its zeros, include complex conjugate pairs, and use a known point to determine the leading coefficient. We also apply Descartes’ Rule of Signs and solve a real-world polynomial equation. WATCH THE COMPLETE 5.5 LESSON Part 1 — Remainder Theorem and Factor Theorem Explained:    • Remainder Theorem and Factor Theorem Expla...   Part 2 — Rational Zero Theorem: How to Find All Polynomial Zeros:    • Rational Zero Theorem: How to Find All Pol...   Part 3 — Complex Zeros, Polynomial Construction, and Descartes’ Rule of Signs:    • Complex Zeros, Polynomial Construction, an...   TOPICS IN THIS VIDEO Linear Factorization Theorem Building factors from zeros Zeros with multiplicity Complex Conjugate Theorem Real coefficients and conjugate pairs Finding the leading coefficient from a point Writing factored and general forms Descartes’ Rule of Signs Possible positive real zeros Possible negative real zeros Nonreal complex-zero counts Solving a polynomial application Rejecting nonphysical solutions REVIEW PARTS 1 AND 2 Part 1 — Remainder and Factor Theorems:    • Remainder Theorem and Factor Theorem Expla...   Part 2 — Rational Zero Theorem:    • Rational Zero Theorem: How to Find All Pol...   PRINTABLE RESOURCES Practice worksheet and complete solution key: Coming soon No-Mystery Mathematics Gumroad storefront: https://nomysterymathematics.gumroad.... COURSE LINKS Complete Precalculus playlist:    • Complete Precalculus Course: Step-by-Step ...   YouTube channel:    / @nomysterymathematics   No-Mystery Mathematics Math made clear, one step at a time. Understand the why, not just the steps.