Science, Tech, Math › Math What Are Polynomials? Share Flipboard Email Print Jose Luis Pelaez Inc / Getty Images Math Pre Algebra & Algebra Math Tutorials Geometry Arithmetic Statistics Exponential Decay Functions Worksheets By Grade Resources View More By Deb Russell Math Expert Deb Russell is a school principal and teacher with over 25 years of experience teaching mathematics at all levels. our editorial process Deb Russell Updated January 17, 2020 Polynomials are algebraic expressions that include real numbers and variables. Division and square roots cannot be involved in the variables. The variables can only include addition, subtraction, and multiplication. Polynomials contain more than one term. Polynomials are the sums of monomials. A monomial has one term: 5y or -8x2 or 3.A binomial has two terms: -3x2 2, or 9y - 2y2A trinomial has 3 terms: -3x2 2 3x, or 9y - 2y2 y The degree of the term is the exponent of the variable: 3x2 has a degree of 2.When the variable does not have an exponent - always understand that there's a '1' e.g., 1x Example of Polynomial in an Equation x2 - 7x - 6 (Each part is a term and x2 is referred to as the leading term.) Term Numerical Coefficient x2-7x-6 1 -7 -6 8x2 3x -2 Polynomial 8x-3 7y -2 NOT a Polynomial The exponent is negative. 9x2 8x -2/3 NOT a Polynomial Cannot have division. 7xy Monomial Polynomials are usually written in decreasing order of terms. The largest term or the term with the highest exponent in the polynomial is usually written first. The first term in a polynomial is called a leading term. When a term contains an exponent, it tells you the degree of the term. Here's an example of a three-term polynomial: 6x2 - 4xy 2xy: This three-term polynomial has a leading term to the second degree. It is called a second-degree polynomial and often referred to as a trinomial.9x5 - 2x 3x4 - 2: This 4 term polynomial has a leading term to the fifth degree and a term to the fourth degree. It is called a fifth degree polynomial.3x3: This is a one-term algebraic expression that is actually referred to as a monomial. One thing you will do when solving polynomials is combined like terms. Like terms: 6x 3x - 3xNOT like terms: 6xy 2x - 4 The first two terms are like and they can be combined: 5x2 2x2 - 3 Thus: 10x4 - 3 Look Up Math Definitions With This Handy Glossary Dividing Monomials in Basic Algebra Learn to Simplify Algebra Equations With the Distributive Property Law What Is a Binomial? 5 Great Resources to Help You Learn Algebra in 2020 5 Adding and Subtracting Polynomial Worksheets What Is the Degree of a Polynomial? Here's How Equivalent Systems of Equations Work Express Your Mathematical Self: How to Write Algebraic Expressions Struggling to Solve Algebra Word Problems? The 8 Best Scientific Calculators of 2020 What Are the Math Skills You Need to Succeed in an MBA Program? Suggested Courses for a High School Math Curriculum 7th Grade Math Concepts Improve Algebra Achievement With These Top 5 Apps What Formula Generates the Bell Curve in Statistics?