A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

For example, an expression such as:

$3x^2\; -\; 5x\; +\; 7$

is a polynomial.

Whereas:

$3x^2\; -\; 5/x\; +\; 7\backslash sqrt\{x\}$

is not a polynomial, because it includes division by a variable ($5/x$) and a fractional exponent ($\backslash sqrt\{x\}\; =\; x^\{1/2\}$).

Key characteristics of polynomials:

• They can have variables, coefficients, and constants.
• The exponents of the variables must be non-negative integers.
• They do not involve division by a variable.

A polynomial can have one or more terms. Each term consists of a coefficient multiplied by a variable raised to a non-negative integer power. Polynomials are fundamental in algebra and are used extensively in various areas of mathematics, science, and engineering.

More information can be found on Wikipedia: Polynomial.