Polynomials are mathematical expressions consisting of variables, constants, and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. They are widely studied in mathematics for their role in algebra, calculus, and other fields. Polynomials can be used to model real-world problems, represent functions, and solve equations. Key concepts related to polynomials include degree, leading coefficient, roots, zeros, factoring, and graphing. Researchers study polynomials to understand their properties, applications, and relationships with other mathematical structures.