What is the Difference Between Polynomial and Monomial?
🆚 Go to Comparative Table 🆚The main difference between a polynomial and a monomial lies in the number of terms they contain. Here is a summary of their key differences:
Monomial:
- A monomial is an algebraic expression containing only one term.
- Monomials can include numbers, whole numbers, variables, and variables multiplied together.
- A monomial cannot have fractional or negative exponents.
- Examples of monomials include 6xy³ or 5x.
Polynomial:
- A polynomial is an algebraic expression that represents the sum of one or more monomials.
- Polynomials can contain multiple terms, each called a "term" or "monomial".
- A polynomial has non-negative integral exponents of variables.
- Examples of polynomial expressions include 7a² + 18a and -2x⁵ + 17x³ - 9x.
In summary, a monomial contains only one term, while a polynomial is a sum of multiple terms, called monomials.
Comparative Table: Polynomial vs Monomial
The main difference between a polynomial and a monomial lies in the number of terms they contain. A polynomial is a mathematical expression that contains two or more terms, while a monomial is a single-term expression. Here is a comparison table highlighting the differences between polynomials and monomials:
Feature | Polynomials | Monomials |
---|---|---|
Number of Terms | Contains two or more terms | Contains a single term |
Structure | Made up of multiple terms separated by + or - | Single term with coefficients and variables |
Degree | The highest exponent of the variable(s) | The exponent of the variable(s) |
In summary, polynomials are mathematical expressions with two or more terms, while monomials are single-term expressions. Monomials are also considered a type of polynomial, but not all polynomials are monomials.
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