How to Find Rational Roots of Polynomials

Miacademy & MiaPrep Learning Channel

This educational video provides a comprehensive guide to the Rational Root Theorem, a fundamental concept in Algebra 2 and Pre-Calculus. The lesson begins by addressing a common problem in polynomial factoring: how to find roots when no starting factor is provided. Using clear visual aids and step-by-step examples, the narrator explains how to identify potential rational roots by analyzing the leading coefficient and the constant term of a polynomial function. The video breaks down the standard form of a polynomial and introduces the formula ±p/q, where 'p' represents factors of the constant term and 'q' represents factors of the leading coefficient. Viewers are guided through two complete examples: a cubic polynomial and a quartic polynomial. The lesson demonstrates how to list all possible rational roots, eliminate duplicates, and efficiently test these candidates using synthetic division to find the actual zeros of the function. Ideal for high school math classrooms, this video connects previous knowledge of synthetic division with new strategies for polynomial analysis. It emphasizes the importance of systematic checking and perseverance in problem-solving. Teachers can use this resource to introduce the theorem, model the process of testing roots, or as a review tool for students mastering higher-level algebraic concepts.