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Each monomial within a polynomial has a characteristic called degree. This degree is determined by the powers (exponents) of its variables.
If a monomial has only one variable, like , its degree is the exponent of that variable, which is .
Examples:
If a monomial has more than one variable, its degree is the sum of all the variable exponents.
Examples:
What about a constant (a number without variables), like ? A non-zero constant is considered to have a degree of , because we can write it as (since ).
Here is a summary of monomial degree examples in a table:
| Monomial | Degree | Explanation |
|---|---|---|
| The exponent of is . | ||
| The exponent of is . | ||
| Sum of exponents . | ||
| Non-zero constant. Can be written as . |
The degree of a monomial (with a non-zero coefficient) is the sum of the exponents of all its variables. For a monomial , its degree is .
Once we know how to determine the degree of each monomial (term), finding the degree of a polynomial becomes easier.
The degree of a polynomial is the highest degree among all the terms (monomials) that make up the polynomial.
Steps to determine the degree of a polynomial:
Example :
Determine the degree of the following polynomial:
The highest degree among the terms is . Therefore, the degree of this polynomial is .
Example :
Determine the degree of the following polynomial:
The highest degree among the terms is . Therefore, the degree of this polynomial is .
Example :
Determine the degree of the following polynomial:
The highest degree is . Therefore, the degree of this polynomial is .
The degree of a polynomial is the highest degree of its terms.
Is the degree of equal to , since can be written as ?
Generally in mathematics:
However, for the high school level, understanding that non-zero constants have degree and the degree of a polynomial is the highest degree of its terms is sufficient.
| Sum of exponents . |
