The function f(x) = a_n x^n + a_n-1 x^n-1 + \ldots + a_1 x + a_0 is a polynomial of degree n . Here, a_n, a_n-1, \ldots, a_0 are constants called coefficients, and x is the variable. The highest power of x determines the degree of the polynomial, which influences its shape and behavior. Polynomials are widely used in mathematics and various fields, including physics, engineering, and economics. They can model a range of real-world phenomena, such as projectile motion or financial growth. Understanding polynomials helps in solving equations and analyzing functions effectively.