Polynomials are classified based on the number of terms they contain.
A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and non-negative integer exponents. The number of these terms directly affects how we name the polynomial. Here’s a breakdown:
- Monomial: A polynomial with only one term. Examples:
5x,7,3x²y - Binomial: A polynomial with two terms. Examples:
x + 2,3y - 5x,a² + b² - Trinomial: A polynomial with three terms. Examples:
x² + 2x + 1,a + b + c,4p² - 7p + 2
For polynomials with more than three terms, there isn't a specific, commonly used name. Instead, they are simply referred to as a "polynomial with n terms," where n represents the number of terms. For example, a polynomial with four terms is simply called a "polynomial with four terms."
Here's a table summarizing the classification:
| Number of Terms | Name | Example |
|---|---|---|
| 1 | Monomial | 5x |
| 2 | Binomial | x + 2 |
| 3 | Trinomial | x² + 2x + 1 |
| 4 or more | Polynomial | x³ + 2x² - x + 7 (4 terms) |
In summary, polynomials are classified by the number of terms as monomials (one term), binomials (two terms), or trinomials (three terms). For polynomials with four or more terms, we generally just specify the number of terms.
