Understanding Polynomials: A Primer on Arithmetic Operations, Degrees, and Terms

Polynomial

An algebraic expression that is the sum of one or more terms (or monomials)

A polynomial is a mathematical expression made up of variable(s) and coefficient(s), where both the variables and coefficients are combined using only the arithmetic operations of addition, subtraction, and multiplication. The variables in a polynomial can only have whole number exponents that are non-negative integers, meaning they cannot be fractions or negative numbers. The highest exponent of the variable in a polynomial is also known as its degree.

For example, a polynomial in x can be written as:

P(x) = aₙₓⁿ + aₙ₋₁ₓⁿ⁻¹ + … + a₂x² + a₁x + a₀

Here, a₀, a₁, a₂,…, aₙ are constants called coefficients and n represents the degree of the polynomial.

The terms of a polynomial are composed of a coefficient and a variable raised to a power (exponent) and in the example above, the term a₂x² is an example of a second-degree term.

Polynomials are commonly used in algebraic operations, particularly in solving equations and graphing functions, making them an important concept in mathematics.

More Answers: