POLYNOMIAL EXPRESSION Meaning and
Definition
-
A polynomial expression refers to a mathematical expression that comprises terms involving variables, constants, and positive integer exponents. It is an algebraic expression that involves addition, subtraction, and multiplication, but not division or the square root of variables. Polynomial expressions often function as models or representations of real-world situations and are fundamental to algebraic analysis and problem-solving.
A polynomial expression is composed of one or more terms, where each term consists of a coefficient and a variable raised to a non-negative power. The coefficient represents the constant factor or numerical value attached to the variable. The variable, on the other hand, denotes an unknown quantity or a symbol representing a number that can vary.
Additionally, the terms within a polynomial expression are combined by using either addition or subtraction operations. However, it should be noted that the variables in a polynomial expression are not allowed to appear in the denominator or under a radical sign. Moreover, the exponents associated with variables must be whole numbers.
The polynomial expression can be categorized based on the number of terms it contains. For instance, a polynomial expression with one term is referred to as a monomial, while two terms constitute a binomial, and three terms form a trinomial. In general, any expression consisting of more than three terms is known as a polynomial.
In conclusion, a polynomial expression is a mathematical expression that encompasses combinations of coefficients, variables, and non-negative exponents. By understanding and manipulating polynomial expressions, mathematicians can solve equations, analyze patterns, and predict behavior in various fields of study.
Etymology of POLYNOMIAL EXPRESSION
The word "polynomial" comes from the Latin word "polynomius", which is derived from the Greek words "poly" meaning "many" and "nomos" meaning "term" or "rule". In mathematics, a polynomial is an expression consisting of variables (representing unknowns) and coefficients (representing constants), combined using addition, subtraction, and multiplication, where variables have non-negative integer exponents. The term "expression" simply refers to a mathematical phrase or combination of mathematical symbols. So, the etymology of the word "polynomial expression" combines the Latin and Greek roots, reflecting the idea of a mathematical expression composed of multiple terms.
