A polynomial is an expression built from variables and constants using addition, subtraction, and multiplication, with whole-number exponents — like 3x² + 2x − 5. The pieces have names worth knowing.
- Term — a single piece separated by + or − (3x², 2x, and −5 are three terms).
- Coefficient — the number multiplying a variable (3 and 2 above).
- Constant — a term with no variable (−5).
- Degree — the highest exponent (3x² + 2x − 5 has degree 2).
Naming
| Degree | Name | Terms | Name |
|---|---|---|---|
| 1 | Linear | 1 | Monomial |
| 2 | Quadratic | 2 | Binomial |
| 3 | Cubic | 3 | Trinomial |
Standard form writes terms from highest exponent to lowest, which makes it easy to identify the degree and to add, subtract, or compare polynomials by combining like terms (same variable and exponent).
Frequently asked questions
What is the degree of a polynomial? The highest exponent on its variable.
What’s a binomial? A polynomial with two terms.
What is standard form? Terms ordered from highest exponent to lowest.
The degree of a polynomial also tells you the most times its graph can cross the x-axis: a quadratic (degree 2) up to twice, a cubic up to three times. That link between degree and roots is the foundation of solving and graphing them.
Working with polynomials follows simple rules too. To add or subtract them, combine like terms — matching variables and exponents — so 3x² + 2x² becomes 5x². To multiply, distribute every term in one across every term in the other, then collect like terms. Keeping everything in standard form throughout makes those steps far less error-prone.