Polynomials and Quadratics - Advanced

This math unit starts with the fundamental skills of expanding algebraic expressions and applying the distributive property to simplify polynomial terms. Students initially practice multiplying a constant or variable with binomial expressions, moving towards identifying equivalent expressions with a focus on polynomials and quadratic functions. The complexity gradually increases as learners manipulate expressions involving same or different variables. Further along in the unit, students delve into more sophisticated tasks such as multiplying and removing variables from bracketed terms, including applications of the FOIL method and reinforcing the correct handling of signs when dealing with squared variables and constants. The unit transitions into quadratic equations, where students factor and simplify quadratic expressions, including those with coefficients, thus enhancing their algebraic manipulation skills. Towards the end of the unit, advanced concepts such as completing the square are introduced, focusing on transforming quadratic expressions into perfect square trinomials. This cements a deeper understanding of polynomials and quadratic equations, preparing students for more complex algebraic problems.