Mastering Synthetic Division to Factor Polynomials

Miacademy & MiaPrep Learning Channel

This educational video provides a comprehensive guide to synthetic division, a streamlined method for dividing polynomials that serves as a faster alternative to traditional long division. The video begins by reviewing the Fundamental Theorem of Algebra and the importance of factoring polynomials to find their roots. Using a numerical analogy with prime factorization, the narrator establishes the logic behind dividing by a known factor to simplify a complex problem. The core of the video is a step-by-step tutorial on setting up and executing synthetic division, explicitly detailing the rules for the divisor and the "drop, multiply, add" algorithm. The content moves beyond just the procedure by comparing synthetic division side-by-side with polynomial long division to explain *why* it works, highlighting efficiency and the removal of variables during calculation. A critical segment addresses common pitfalls, such as the necessity of using placeholder zeros for missing terms in a polynomial (e.g., a missing x-cubed term). The narrator guides viewers through a practice problem involving a quartic polynomial, ensuring they understand how to interpret the resulting coefficients and remainder. This resource is highly valuable for high school Algebra II and Pre-Calculus classrooms. It breaks down a typically abstract algorithmic process into digestible steps with clear visual aids. Teachers can use this video to introduce the concept of synthetic division, reinforce the importance of placeholders, or facilitate a flipped classroom model where students learn the mechanics at home and practice applying the Rational Root Theorem in class.