Polynomials Factoring - Factor Theorem and Synthetic Division - Intro

This math unit begins by focusing on the factoring of cubic polynomials. Initially, students learn to factor cubic polynomials by grouping, breaking down quadratic factors into linear factors, and determining the correctness of these steps through true/false questions. As the unit progresses, the focus shifts towards more advanced polynomial operations using the Factor Theorem and Synthetic Division. Students practice finding the remainder of polynomial division when divided by a binomial, and identifying coefficients given a binomial factor, enhancing their understanding of the relationships within polynomial expressions. Further development in the unit introduces synthetic division, where students progressively learn and practice setting up division with varying complexities, from handling single coefficients in a specific order to managing full setup with random coefficients. Each step equips them with skills needed to efficiently simplify polynomial division, leading to the final setup and extraction of results. Finally, the unit delves into the Rational Root Theorem, guiding students through identifying constant terms, possible rational roots, and listing all potential rational roots of polynomial equations, rounding out their competence in polynomial factoring and analysis.Skills you will learn include:

• The factor theorem
• The remainder theorem
• Finding unknown coefficients