Monomial

A monomial is an algebraic expression consisting of a coefficient multiplied by variables raised to nonnegative integer powers. It has one term, with no variables in denominators or radicals.

Coefficient: A coefficient is a numerical factor multiplying a variable or algebraic expression. The coefficient supplies the numerical factor in a monomial.
Multiplication of monomials: Multiplication of monomials multiplies coefficients and adds exponents of matching variables. This operation preserves monomial form by combining like variable factors.
Polynomial: A polynomial is a finite sum of monomials with coefficients and nonnegative integer exponents. Polynomials are built by adding monomials.
Binomial: A binomial is a polynomial with exactly two nonzero terms. Unlike a monomial, a binomial contains two terms.
Exponent: An exponent indicates how many times its base is multiplied by itself. Each variable’s exponent must be a nonnegative integer in a monomial.
Division of monomials: Division of monomials divides coefficients and subtracts exponents of matching variables, when defined. Division can produce negative exponents, taking the result outside ordinary polynomial monomials.
Monomial basis: A monomial basis is the collection of powers of variables used to express polynomials or functions. Polynomial coefficients record the weights of individual monomial terms.
Trinomial: A trinomial is a polynomial with exactly three nonzero terms. It differs from a monomial by containing three terms.
Variable (mathematics): A variable is a symbol representing a quantity that can take different values. Variables are the symbols raised to powers in a monomial.
Like terms: Like terms have identical variable factors raised to identical powers. Only monomials with the same variable part combine by adding coefficients.

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