Identify monomials

Learning Objectives Define the term 'monomial' in their own words. Identify the coefficient, variable(s), and degree of a given monomial. Distinguish between expressions that are monomials and those that are not. By the end of of this lesson, students will be able to explain why an expression with a variable in the denominator is not a monomial. Explain why an expression with a negative or fractional exponent on a variable is not a monomial. Classify constants as monomials with a degree of zero. What's the simplest 'building block' you can imagine in algebra? 🧱 Let's explore the single-term expressions that form the foundation of all polynomials! This tutorial will teach you how to identify monomials, which are the fundamental units of polynom...

TermDefinitionExample MonomialA number, a variable, or the product of a number and one or more variables with non-negative integer exponents.5x^2, -8, 3ab^4 CoefficientThe numerical factor of a monomial. It's the number being multiplied by the variable(s).In the monomial 7y^3, the coefficient is 7. VariableA symbol, usually a letter, used to represent an unknown value or a quantity that can change.In the monomial -4x^2y, the variables are x and y. ExponentA number indicating how many times to multiply a base (the variable) by itself. In a monomial, exponents must be non-negative integers (0, 1, 2, 3, ...).In the monomial 2z^5, the exponent is 5. Degree of a MonomialThe sum of the exponents of all the variables in the monomial. A constant has a degree of 0.The degree of 6x^2y^3 is 2 +...

The Monomial Checklist An expression is a monomial if it meets ALL of these conditions: 1. It is a single term. 2. It has no variables in the denominator. 3. All variable exponents are non-negative integers (0, 1, 2, ...). Use this checklist to systematically determine if any given algebraic expression qualifies as a monomial. If it fails even one condition, it is not a monomial. The Degree Formula For a monomial of the form ax^m y^n, the degree is m + n. To find the degree of a monomial, simply identify the exponent for each variable and add them all together. If a variable has no visible exponent, its exponent is 1. The 'Not a Monomial' Red Flags An expression is NOT a monomial if you see: 1. Division by a variable (e.g., \frac{5}{x}). 2. A negative exponen...