Polynomial

A polynomial is an expression formed from constants and variables using addition, subtraction, multiplication, and nonnegative integer powers of variables. Its terms have fixed coefficients and nonnegative integer exponents.

Monomial: An algebraic expression consisting of a coefficient multiplied by variables raised to nonnegative integer powers. Each term of a polynomial is a monomial.
Polynomial addition: The operation of adding polynomials by summing coefficients of like terms. Addition combines terms without introducing new exponent types.
Polynomial function: A function defined by evaluating a polynomial at each input. The expression defines a function once its variables are assigned input values.
Laurent polynomial: A finite sum of terms whose variable exponents may be negative integers. Negative powers distinguish Laurent polynomials from ordinary polynomials.
Coefficient: A numerical or symbolic factor multiplying a variable or product of variables. Coefficients set the scale of each polynomial term.
Polynomial multiplication: The operation of multiplying polynomials by distributing products across their terms. Multiplication adds exponents of matching variables and expands products.
Polynomial interpolation: The construction of a polynomial that matches specified data points. A polynomial can reconstruct a curve passing through a finite set of observations.
Rational expression: An algebraic expression formed as a quotient of polynomials. Variable denominators generally take expressions outside the polynomial class.
Exponent: A number indicating how many times a base is used as a factor. Polynomial exponents on variables must be nonnegative integers.
Polynomial division: A procedure for dividing one polynomial by another, producing a quotient and possibly a remainder. Division can reveal factors or leave a remainder rather than another polynomial.

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