What is the Difference Between Polynomial and Monomial?

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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.