Degree of a Polynomial – Definition, Types, Examples | How to find the Degree of a Polynomial?

The Degree of a Polynomial is defined as the highest power of the variable in a given polynomial expression. Polynomial is the combination of two or more algebraic terms which contain different powers of the same variable. Also, a polynomial is a combination of monomials. The degree is defined as the highest exponential power in the polynomial. All the Degree of Polynomial concepts and worksheets are given in 6th Grade Math articles.

Also, find:

• Addition of Polynomials
• Subtraction of Polynomials
• Worksheet on Degree of a Polynomial

What is the Degree of a Polynomial?

It is the greatest power of a variable presented in a polynomial equation. Here the degree indicates the highest power in the polynomial. A polynomial can have a single term or more than a single term in it. The variable which presents in a polynomial with the highest degree is considered the degree of the polynomial.

Examples: (i) The degree of the polynomial 5a⁴ + 3a³+ 3 is 4.
(ii) The degree of the polynomial 4m⁷+ 7m³ + 3m + 2 is 7.

Degree of a Zero Polynomial

A zero polynomial is the polynomial that consists of all the coefficients equal to zero. Therefore, the degree of the zero polynomial is either undefined or set to -1.

Degree of a Constant Polynomial

The constant polynomials will have only constants. it will not have any variables. If P(x) = 8, then it can write as 8x⁰ and the degree of the constant polynomial is zero.

How to Find the Degree of a Polynomial?

While finding a degree of a polynomial, you can different variables with different exponents. To find the exact degree of the polynomial, you must follow the below procedure.

(i) Firstly, from the given polynomial, separate the like terms along with their variable terms.
(ii) Skip all the coefficients.
(iii) Make sure to arrange all the variables in descending order according to their powers.
(iv) Finally, note down the degree of the polynomial.

Types of Polynomials Based on Degree

The below table will let you know the degree of a polynomial and also the name of the polynomial according to its degree.

Degree of a Polynomial	Name of the Polynomial
0	Constant Polynomial
1	Linear Polynomial
2	Quadratic Polynomial
3	Cubic Polynomial
4	Quadratic Polynomial

Degree of Polynomial Function Examples

Check out how to solve the degree of polynomial problems with a clear explanation.

Question 1.
What is the degree of the polynomial 4a² – 9a⁷ + 3a⁸

Solution:
Given polynomial is 4a² – 9a⁷ + 3a⁸.
The given polynomial consists of three terms and a single variable a. Find out all the terms and their exponents.
Now, find every term exponent separately.

• The first term of the given polynomial is 4a² and the exponent of 4a² is 2.
• Next, the second term of the given polynomial is 9a⁷ and the exponent of 9a⁷ is 7.
• The third term of the given polynomial is 3a⁸ and the exponent of 3a⁸ is 8.

The greatest exponent is 8. Therefore, the degree of the polynomial 4a² – 9a⁷ + 3a⁸ is 8.

Question 2.
Find the degree of the polynomial 1 + 4m – 6m² + 17m³ – 2m⁴.

Solution:
Given polynomial is 1 + 4m – 6m² + 17m³ – 2m⁴.
The given polynomial consists of five terms and a single variable m. Find out all the terms and their exponents.
Now, find every term exponent separately.

• The first term of the given polynomial is 1 (for constant, we can take the variable as m⁰) and the exponent of m⁰ is 0.
• Next, the second term of the given polynomial is 4m and the exponent of 4m is 1.
• The third term of the given polynomial is 6m² and the exponent of 6m² is 2.
• The fourth term of the given polynomial is 17m³ and the exponent of 17m³ is 3.
• The fifth term of the given polynomial is 2m⁴ and the exponent of 2m⁴ is 4.

The greatest exponent is 4. Therefore, the degree of the polynomial 1 + 4m – 6m² + 17m³ – 2m⁴ is 4.

Question 3.
Find the degree of the polynomial consisting of two variables. The polynomial is 3xy – 2x + 3y -2.

Solution:
Given polynomial is 3xy – 2x + 3y -2.
The given polynomial consists of four terms and consists of two variables x and y. Find out all the terms and their exponents.
Now, find every term exponent separately.

• The first term of the given polynomial is 3xy and the exponent of 3xy is 2.
  (Note: If mn are two variables, then the degree of them becomes the addition of their exponents i.e, 1 + 1 = 2)
• Next, the second term of the given polynomial is 2x and the exponent of 2x is 1.
• The third term of the given polynomial is 3y and the exponent of 3y is 1.
• The fourth term of the given polynomial is 2 (for constant, we can take the variable as x⁰y⁰ and the exponent of 2 is 0 + 0 = 0.

The greatest exponent is 2. Therefore, the degree of the polynomial consisting of two variables 3xy – 2x + 3y -2 is 2.

Question 4.
Find the degree of the polynomial 9x³ – 17x⁵ + 34x + 5.

Solution:
Given polynomial is 9x³ – 17x⁵ + 34x + 5.
The given polynomial consists of four terms and consists of a single variable x. Find out all the terms and their exponents.
Now, find every term exponent separately.

• The first term of the given polynomial is 9x³ and the exponent of 9x³ is 3.
• Next, the second term of the given polynomial is 17x⁵ and the exponent of 17x⁵ is 5.
• The third term of the given polynomial is 34x and the exponent of 34x is 1.
• The fourth term of the given polynomial is 5 (for constant, we can take the variable as x⁰ and the exponent of 5 is 0.

The greatest exponent is 5. Therefore, the degree of the polynomial 9x³ – 17x⁵ + 34x + 5 is 5.

Question 5.
Find the degree of the polynomial consisting of two variables. The polynomial is 6l³ + 2l – 3m + 5lm -7.

Solution:
Given polynomial is 6l³ + 2l – 3m + 5lm -7.
The given polynomial consists of five terms and consists of two variables l and m. Find out all the terms and their exponents.
Now, find every term exponent separately.

• The first term of the given polynomial is 6l³ and the exponent of 6l³ is 3.
  Next, the second term of the given polynomial is 2l and the exponent of 2l is 1.
• The third term of the given polynomial is 3m and the exponent of 3m is 1.
• The fourth term of the given polynomial is 5lm and the exponent of 5lm is 1 + 1 = 2.
  (Note: If mn are two variables, then the degree of them becomes the addition of their exponents i.e, 1 + 1 = 2)
• The fifth term of the given polynomial is 7 (for constant, we can take the variable as x⁰y⁰) and the exponent of 7 is 0 + 0 = 0.

The greatest exponent is 3. Therefore, the degree of the polynomial consisting of two variables 6l³ + 2l – 3m + 5lm -7 is 3.

Question 6.
Find the degree of a polynomial 2p + 3p².

Solution:
Given polynomial is 2p + 3p².
The given polynomial consists of two terms and a single variable p. Find out all the terms and their exponents.
Now, find every term exponent separately.

• The first term of the given polynomial is 2p and the exponent of 2p is 1.
• Next, the second term of the given polynomial is 3p² and the exponent of 3p² is 2.

The greatest exponent is 2. Therefore, the degree of the polynomial 2p + 3p² is 2.

FAQs on Degree of a Polynomial

1. What is the Degree of a Polynomial?

The Degree of a Polynomial can explain with the highest power of any variable that presents in a polynomial. The highest power will be treated as the degree of the polynomial.

2. What is a 3rd Degree Polynomial?

The 3rd Degree Polynomial is also called the cubic polynomial.

3. What is the Degree of a Quadratic Polynomial?

A Quadratic Polynomial is a type of polynomial that consists of a degree 4. So, a quadratic polynomial has a degree of 4.

4. What is the degree of the multivariate term in a polynomial?

If in a polynomial single term, m and n are the exponents, then the degree of a term in the polynomial will write as m + n. For example, 3p²q⁴ is a term in the polynomial, the degree of the term is 2+4, which is equal to 6.

Hence, the degree of the multivariate term in the polynomial is 6.

5. Find the Degree of this Polynomial: 9l³ + 7l⁵ – 5l² + 3l -2

To find the Degree of this Polynomial: 9l³ + 7l⁵ – 5l² + 3l -2, combine the like terms and then arrange them in descending order of their power.
9l³ + 7l⁵ – 5l² + 3l -2 = 7l⁵ + 9l³ + – 5l² + 3l -2

Thus, the degree of the polynomial is 5.

Summary

The degree of a polynomial concept solved problems and their explanation, and everything related to it is given in this article. So, to learn the complete concept, go through every part of the given article. Practice all the problems on your own and check the answers to know your preparation status.