How to Factor Polynomials Using Five Different Methods

Miacademy & MiaPrep Learning Channel

This instructional video serves as a comprehensive review of polynomial factoring techniques by presenting a single "mega-problem" composed of five distinct expressions multiplied together. The instructor, Randy, guides viewers through tackling each expression individually, demonstrating a specific factoring method for each: Greatest Common Factor (GCF), Difference of Squares, Sum-Product Pattern, Perfect Square Trinomials, and Factor by Grouping. This structure allows students to see the differences between polynomial forms side-by-side. The video explores key algebraic themes including identifying polynomial structures, determining the appropriate factoring strategy, and the mechanics of breaking down expressions. It covers the logic behind finding two numbers that multiply to a product and add to a sum, the special properties of square numbers, and how to handle four-term polynomials using grouping. The instructor also emphasizes the importance of verifying answers by multiplying factors back together. For educators, this video is an excellent synthesis tool or review resource for an Algebra unit. It moves beyond teaching isolated skills to helping students practice "diagnosis"—looking at a problem and deciding which tool to use. It can be used as a summary lesson before a test, a flipped classroom resource, or a remediation tool for students struggling to differentiate between factoring methods. The clear, step-by-step handwriting and logical pacing make it accessible for high school math students.