What is Trinomial?
Consisting of or relating to three names or terms. A polynomial with three terms.
A trinomial is a type of polynomial that has exactly three terms. These three terms are separated by addition or subtraction signs. Each term can be a number, a variable, or a product of numbers and variables.
For example, expressions like x² + 5x + 6, 3a² – 2a + 1, and 4x + 2y – 3 are all trinomials. Each of these expressions has three distinct terms connected by plus or minus signs.
In contrast, expressions like x + 3 are not trinomials because they have only two terms—those are called binomials. Similarly, 5x is a monomial because it consists of just one term. A trinomial always has exactly three parts; no more, no less.
Trinomials often appear in algebraic problems where students practice factoring, expanding, and solving equations. They are especially important for:
- Factoring quadratic expressions
- Expanding squared binomials
- Solving quadratic equations
When Do Students Learn About Trinomials?
Students are introduced to trinomials when they begin working with polynomials and factoring in algebra. This typically starts in middle school and continues into high school.
Grades 6–8 – Introduction to Trinomials
In Grades 6–8, students learn to identify trinomials and practice simple addition and subtraction with three-term expressions.
Grades 9+ – Working with Trinomials in Algebra
In Grades 9+, students learn to multiply, divide, and factor trinomials. They also solve quadratic equations that are expressed as trinomials.
