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◉ Science·2 min·Updated Mar 12, 2026

What is Polynomial?

Polynomial Expression

Quick Answer

A polynomial is a mathematical expression that consists of variables raised to whole number powers and coefficients. It can be as simple as a single term or a complex combination of multiple terms. Polynomials are fundamental in algebra and are used in various fields such as physics and engineering.

Overview

Polynomials are expressions made up of variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial consists of a coefficient and a variable raised to a non-negative integer exponent. For example, in the polynomial 3x² + 2x - 5, 3, 2, and -5 are coefficients, while x is the variable raised to the powers of 2 and 1 respectively. They work by allowing us to perform calculations and model relationships between quantities. The degree of a polynomial, which is the highest exponent of the variable, helps determine its shape and behavior on a graph. For instance, a second-degree polynomial like a parabola can represent the trajectory of an object in motion, making it useful in physics for calculating projectile paths. Polynomials matter because they are foundational in various areas of mathematics and science. They are used in calculus to find rates of change and in statistics for regression analysis. Understanding polynomials can help in solving real-world problems, such as optimizing costs in business or predicting trends in data.

Frequently Asked Questions

Polynomials can be classified based on their degree. A polynomial with one term is called a monomial, two terms is a binomial, and three terms is a trinomial. Higher degree polynomials can have even more terms.
To add or subtract polynomials, you combine like terms, which are terms that have the same variable raised to the same power. For example, if you have 2x² + 3x and 4x² - 5x, you would combine 2x² and 4x² to get 6x², and 3x and -5x to get -2x.
No, polynomials cannot have negative or fractional exponents. Each term must have non-negative integer exponents, which means they can only be whole numbers like 0, 1, 2, etc.