Science, Tech, Math › Math What Are Polynomials? Introduction to 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 Deb Russell is a school principal who has taught mathematics at all levels. She is also a freelance writer with more than 14 years of experience. Updated March 24, 2019 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 a 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 which is actually referred to as a monomial. One thing you will do when solving polynomials is combine like terms. Like terms: 6x 3x - 3x NOT like terms: 6xy 2x - 4 The first two terms are like and they can be combined: 5x2 2x2 - 3 Thus: 10x4 - 3 Now you're ready to start adding polynomials. Continue Reading Learn to Simplify Algebra Equations With the Distributive Property Law Look Up Math Definitions With This Handy Glossary What Is a Binomial? Dividing Monomials in Basic Algebra What Is the Degree of a Polynomial? Suggested Courses for a High School Math Curriculum 5 Adding and Subtracting Polynomial Worksheets Express Your Mathematical Self: How to Write Algebraic Expressions 6 Great Resources to Help You Learn Algebra Here's How Equivalent Systems of Equations Work Improve Algebra Achievement With These Top 5 Apps What Does the Word Algebra Mean, Anyway? Using FOIL to Solve Algebraic Equations Practice Your Algebraic Expressions With These Pre Algebra Worksheets Core Math Concepts Every 11th Grader Should Know Are We Living in the Age of Algorithims?