Algebra Vocabulary: Key Terms, Definitions, and Examples Every Student Should Know
Algebra vocabulary is the shared language of every problem on this site. A variable is a letter that stands in for an unknown number, a coefficient is the number multiplied by that variable, and a constant is a fixed number with no variable attached. Once you can name the parts of an expression, you can tell an expression from an equation, read a polynomial, and describe a graph. Use the grouped definitions below, then turn a weak topic into practice.
Core Terms
Every expression is built from the same small parts.
- Variable — a letter that represents an unknown or changing value. In 3x + 2, x is the variable.
- Coefficient — the number multiplied by the variable. In 3x + 2, the coefficient of x is 3.
- Constant — a fixed number with no variable. In 3x + 2, the constant is 2.
- Term — a single number, variable, or product of numbers and variables. In 3x + 2, the terms are 3x and 2.
- Like terms — terms with the same variable part. 3x and 5x are like terms; 3x and 5y are not.
Expressions vs Equations vs Inequalities
The fastest way to confuse algebra is to mix up these three.
- Expression — a combination of terms with no equals sign. 3x + 2 is an expression; it can be simplified but not "solved."
- Equation — a statement that two expressions are equal, so it always has an equals sign. 3x + 2 = 11 is an equation.
- Inequality — a comparison using <, >, ≤, ≥, or ≠. 3x + 2 > 11 is an inequality.
Only equations and inequalities have a solution set. An expression by itself is just a phrase.
Exponent and Polynomial Vocabulary
When powers and sums appear, these are the words you need.
- Base — the number being raised to a power. In x^4, x is the base.
- Exponent — the power to which the base is raised. In x^4, 4 is the exponent.
- Monomial — a single term, such as 5x^2.
- Binomial — a polynomial with two terms, such as x + 3.
- Trinomial — a polynomial with three terms, such as x^2 - 5x + 2.
- Degree — the highest exponent in a polynomial. x^2 - 5x + 2 has degree 2.
The exponents guide explains the power rules, and the polynomials guide builds on this vocabulary.
Function and Graph Vocabulary
Graphs are easier to read once the words are fixed.
- Function — a relation that assigns exactly one output to each input.
- Input / output — the value you start with and the value you get back.
- Domain — the set of all valid inputs.
- Range — the set of all possible outputs.
- Intercept — a point where a graph crosses the x-axis or y-axis.
The functions guide develops domain, range, and graphs in full.
Equation-Solving Vocabulary
Solving has its own precise words.
- Solve — find the value that makes the equation true.
- Isolate — get the variable alone on one side.
- Equivalent equations — equations that have the same solution.
- Solution — the value that satisfies the equation.
For 3x + 2 = 11, isolate 3x by subtracting 2, then divide by 3; the solution is x = 3.
Common Vocabulary Mistakes
- Expression vs equation — no equals sign means it is an expression, not an equation.
- Coefficient vs constant — the coefficient belongs to a variable; the constant stands alone.
- Base vs exponent — x^4 means x multiplied by itself 4 times, not x times 4.
- Domain vs range — domain is inputs, range is outputs.
- Degree vs number of terms — degree is the highest power; a trinomial can have degree 2 or higher.
How to Use This Glossary
Read a category before you work that topic, and keep the Algebra 1 study guide beside you for the full course order. When a word keeps tripping you up, that is the topic to practice next.
Practice Algebra with Gauth
Pick the topic whose vocabulary you just reviewed. Open Gauth Math Courses, select Create Course, and enter a focused request such as "polynomial terms and degree" plus your level. After one short activity, re-read the matching section above before moving on.
Sources and Review
- OpenStax Elementary Algebra 2e, accessed October 14, 2026.