Polynomial Equation

Topic

Equations

Definition

A polynomial equation is an equation that involves a polynomial expression.

Description

Polynomial equations involve expressions that include terms with variables raised to whole-number exponents. For example, the equation 

x² − 4x + 4 = 0 

is a polynomial equation. These equations can be linear, quadratic, cubic, etc., depending on the highest power of the variable.

In real-world applications, polynomial equations are used in various fields such as physics, engineering, and economics to model complex relationships. Understanding polynomial equations helps students solve higher-degree equations and analyze polynomial functions.

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The next section provides a background on polynomials.

What Are Polynomials?

Polynomials Are Made Up of Monomials

A monomial is a single expression that is usually the product of a number and one or more variables raised to a positive exponent power. Read the following definition.

A monomial is an example of a polynomial.

Binomials Are Made Up of Two Monomials

If you combine two monomials, you have a binomial, so long as the two monomials cannot be further added or subtracted. Read the following definition.

Notice how each binomial is made up of two monomials. Here’s an example of two monomials that, when combined, result in a monomial, not a binomial.

Trinomials Are Made Up of Three Monomials

If you combine three monomials, you have a trinomial, so long as the monomials cannot be further added or subtracted. Read the following definition.

Notice how each binomial is made up of three monomials. 

The Degree of a Polynomial

The term with the highest exponent determines the degree of the polynomial.

This is a polynomial of degree 1:

This is a polynomial of degree 2:

This is a polynomial of degree 3: