The polynomial degree refers to the highest power of the variable in a polynomial expression. For example, in the polynomial 3x^4 + 2x^3 - x + 5, the degree is 4 because the term with the highest exponent is 3x^4. This degree helps determine the polynomial's behavior, such as the number of roots it can have. Understanding the degree is essential in various fields, including mathematics and engineering. A polynomial of degree 2 is called a quadratic, and it typically forms a parabolic shape when graphed. Higher degrees can create more complex curves, influencing how we analyze and solve equations.