Polynomial: Definition and Key Concepts
What is a Polynomial?
A polynomial is an algebraic expression that is the sum of monomials. The monomials are connected by addition or subtraction signs.
Examples of Polynomials
- 3x² + 2x − 5 — three terms
- a + b − c — three terms
- 7x³ − 4x² + x − 1 — four terms
- 5y — one term (also a monomial)
NOT Polynomials
- 1/x — variable in denominator
- √x — fractional exponent
- 2x — variable in exponent
Terms of a Polynomial
Each monomial in the polynomial is called a term. The sign before each term belongs to that term.
Example: In the polynomial 5x² − 3x + 7
5x²
First term−3x
Second term+7
Third termNaming Polynomials by Number of Terms
1 Term
Monomial
Single term expression
5x²
2 Terms
Binomial
Two-term expression
x + 3
3 Terms
Trinomial
Three-term expression
x² + 2x + 1
Any Number
Polynomial
Multi-term expression
General term