Polynomials are one of the most frequently studied objects in mathematics. It is no surprise, then, that we devote lengthy chapters to them in both Algebra I and Algebra II. This chapter focuses primarily on the roots or zeros of polynomials, and, in the process, on division of polynomials by binomials.The first section introduces a new form of a polynomial: nested form. Nested form is useful when evaluating polynomial functions by hand. This section explains how to convert a polynomial function to nested form and how to use nested form to evaluate a polynomial function for any value of the variable.The next section explains how to divide a polynomial by a binomial using long division. This is the same long division learned in grade school, but with a variable in the divisor instead of a constant. This section also introduces a shortcut for finding the remainder when a polynomial is divided by a binomial: the Remainder Theorem. The Factor Theorem, which follows from the Remainder Theorem, provides an easy way for determining whether a given binomial is a factor of a given polynomial.