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.

Here's a breakdown of the components:

• Variables: These are symbols (usually letters like x, y, z) that represent unknown or changeable values.
• Coefficients: These are the numbers that multiply the variables. They can be any real number (e.g., 2, -5, 1/2, √3).
• Exponents: These are the powers to which the variables are raised. In a polynomial, exponents must be non-negative integers (e.g., 0, 1, 2, 3, ...).

Examples of Polynomials:

• 3x² + 2x - 1
• y⁴ - 7y + 6
• 5z
• 8 (This is a constant polynomial, where the variable has an exponent of 0)

Examples of Non-Polynomials:

• 3x^-2 (Negative exponent)
• 2√x (Fractional exponent, as √x = x^1/2)
• 1/x (Variable in the denominator, which is equivalent to x^-1)
• sin(x) (Trigonometric function)

Polynomials can have one or more variables. A polynomial with one variable is called a "polynomial in one variable."

Source: MathWorld - Polynomial