How to Completely Factor Monomials

Miacademy & MiaPrep Learning Channel

This video provides a clear and focused tutorial on Algebra concepts, specifically distinguishing between the general concept of factoring and the more precise process of "completely" factoring a monomial. Using the example 12x3y2, the instructor demonstrates multiple ways to validly factor an expression before defining the strict rules required for a complete factorization: prime factorization of coefficients and fully expanded variable exponents. The content covers key mathematical themes including algebraic expressions, exponents, prime numbers, and the structural properties of monomials. It visually breaks down abstract algebraic terms into their component parts, showing how 12 becomes 3*2*2 and how x3 expands to x* x* x. This connects arithmetic skills (factor trees) with algebraic manipulation. For educators, this video serves as an excellent foundational resource for Pre-Algebra or Algebra 1 units. It addresses the common student confusion about when they are "finished" factoring a term. By establishing the rule that complete factorization has only one unique set of components (unlike general factoring), it prepares students for more advanced tasks like finding the Greatest Common Factor (GCF) of polynomials or simplifying rational expressions.