R[x] is a notation used in mathematics to represent the set of all polynomials with real coefficients. In this context, R refers to the set of real numbers, while x is a variable that can take any real value. Polynomials in R[x] can be expressed in the form of a sum of terms, where each term consists of a coefficient from R multiplied by a power of x. The structure of R[x] allows for various operations, such as addition, subtraction, and multiplication of polynomials. This set is fundamental in algebra and is used in many areas of mathematics, including calculus and algebraic geometry, to study polynomial functions and their properties.