How to Factor Out the GCF From Polynomials

Miacademy & MiaPrep Learning Channel

This instructional math video serves as an introductory guide to factoring polynomials by identifying and pulling out the Greatest Common Factor (GCF). Hosted by a narrator named Justin, the video connects this new skill to the previously learned concept of multiplying polynomials, framing factoring as the reverse process of distribution. It systematically breaks down the definitions of 'GCF' and 'Factoring' before demonstrating how to combine these concepts to simplify algebraic expressions. The video explores three distinct examples that increase in complexity. It starts with a simple trinomial requiring only a numerical GCF, progresses to a polynomial with high-degree variables where both numbers and variables must be factored out, and concludes with a 'trick' case involving a negative leading coefficient. Key themes include the relationship between multiplication and factoring, the laws of exponents when dividing variables, and the standard mathematical convention of factoring out negatives to ensure positive leading coefficients. For educators, this video is an excellent primary resource for flipping the classroom or introducing the unit on factoring. It provides clear, step-by-step modeling of procedural skills while explaining the 'why' behind the math. The segment on checking answers by re-distributing reinforces self-correction habits, making it a valuable tool for building student independence in Algebra 1 coursework.