How to Perform Basic Algebra Operations and Factor Polynomials

The Organic Chemistry Tutor

A comprehensive and fast-paced introduction to fundamental algebra concepts, designed for beginners or students needing a robust review. The video systematically covers operations with polynomials, laws of exponents, and various factoring techniques. Using a high-contrast blackboard style, the instructor demonstrates step-by-step procedures for adding, subtracting, and multiplying polynomials, starting from simple binomials and progressing to complex trinomials. The content delves deep into the rules of exponents, explaining the 'why' behind the rules by expanding variable terms (e.g., showing that x cubed is x times x times x). It covers the product rule, quotient rule, power rule, and how to handle negative and zero exponents. The latter third of the video transitions into factoring, introducing the Greatest Common Factor (GCF), the Difference of Squares formula, and the method of Factoring by Grouping for four-term polynomials. This video is an excellent resource for Algebra 1 classrooms. It serves as both a direct instructional tool for introducing new concepts and a reference guide for review. Teachers can utilize the clear, segmented examples to model problems before having students attempt similar ones. The visual explanations of exponent rules are particularly valuable for correcting common student misconceptions, while the factoring segment provides a structured approach to breaking down algebraic expressions.