This unit introduces defining the standard form of a polynomial and its degree. This knowledge will be useful in exploring the Fundamental Theorem of Algebra, which says every non-zero single-variable polynomial, with complex coefficients, has exactly as many complex roots as its degree, if repeated roots are counted up to their multiplicity. Further analysis of polynomials includes end behavior and relative extrema. Besides understanding the graphs of polynomials, analyzing polynomials includes applying and proving the Remainder Theorem. The role of synthetic division versus long division will be key. It will also be necessary to apply and prove the Factor Theorem. Special cases of factoring include sum and difference of two squares and two cubes, grouping, and the Rational Root Theorem. In later mathematics courses, Taylor polynomials will be studied, and it will be necessary to prove theorems about polynomials that are factorable or irreducible over a field.