Degree of a Polynomial

Here we will learn the basic concept of polynomial and the degree of a polynomial.


What is polynomial?

An algebraic expression which consists of one, two or more terms is called a polynomial.


How to find a degree of polynomial?

The degree of the polynomial is the greatest of the exponents (powers) of its various terms.

Examples of polynomials and its degree:

1. For polynomial 2x2 - 3x5 + 5x6.

We observe that the above polynomial has three terms. Here the first term is 2x2, the second term is -3x5 and the third term is 5x6.

Now we will determine the exponent of each term.

(i) the exponent of the first term 2x2 = 2

(ii) the exponent of the second term 3x5 = 5

(iii) the exponent of the third term 5x6 = 6

Since, the greatest exponent is 6, the degree of 2x2 - 3x5 + 5x6 is also 6.

Therefore, the degree of the polynomial 2x2 - 3x5 + 5x6 = 6.



2. Find the degree of the polynomial 16 + 8x – 12x2 + 15x3 - x4.

We observe that the above polynomial has five terms. Here the first term is 16, the second term is 8x, the third term is – 12x2, the fourth term is 15x3 and the fifth term is - x4.

Now we will determine the exponent of each term.

(i) the exponent of the first term 16 = 0

(ii) the exponent of the second term 8x = 1

(iii) the exponent of the third term – 12x2 = 2

(iv) the exponent of the fourth term 15x3 = 3

(v) the exponent of the fifth term - x4 = 4

Since, the greatest exponent is 4, the degree of 16 + 8x – 12x2 + 15x3 - x4 is also 4.

Therefore, the degree of the polynomial 16 + 8x – 12x2 + 15x3 - x4 = 4.


3. Find the degree of a polynomial 7x – 4

We observe that the above polynomial has two terms. Here the first term is 7x and the second term is -4

Now we will determine the exponent of each term.

(i) the exponent of the first term 7x = 1

(ii) the exponent of the second term -4 = 1

Since, the greatest exponent is 1, the degree of 7x – 4 is also 1.

Therefore, the degree of the polynomial 7x – 4 = 1.


4. Find the degree of a polynomial 11x3 - 13x5 + 4x.

We observe that the above polynomial has three terms. Here the first term is 11x3, the second term is - 13x5 and the third term is 4x.

Now we will determine the exponent of each term.

(i) the exponent of the first term 11x3 = 3

(ii) the exponent of the second term - 13x5 = 5

(iii) the exponent of the third term 4x = 1

Since, the greatest exponent is 5, the degree of 11x3 - 13x5 + 4x is also 5.

Therefore, the degree of the polynomial 11x3 - 13x5 + 4x = 5.



5. Find the degree of the polynomial 1 + x + x2 + x3.

We observe that the above polynomial has four terms. Here the first term is 1, the second term is x, the third term is x2 and the fourth term is x3.

Now we will determine the exponent of each term.

(i) the exponent of the first term 1 = 0

(ii) the exponent of the second term x = 1

(iii) the exponent of the third term x2 = 2

(iv) the exponent of the fourth term x3 = 3

Since, the greatest exponent is 3, the degree of 1 + x + x2 + x3 is also 3.

Therefore, the degree of the polynomial 1 + x + x2 + x3 = 3.


6. Find the degree of a polynomial -2x.

We observe that the above polynomial has one term. Here the term is -2x.

Now we will determine the exponent of the term.

(i) the exponent of the first term -2x = 1

Therefore, the degree of the polynomial -2x = 1.

Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials






Algebra Page

6th Grade Page 

From Degree of a Polynomial to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

    Jul 16, 24 02:20 AM

    In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

    Read More

  2. Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

    Jul 16, 24 01:36 AM

    In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

    Read More

  3. Worksheet on Add and Subtract Fractions | Word Problems | Fractions

    Jul 16, 24 12:17 AM

    Worksheet on Add and Subtract Fractions
    Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

    Read More

  4. Comparison of Like Fractions | Comparing Fractions | Like Fractions

    Jul 15, 24 03:22 PM

    Comparison of Like Fractions
    Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2…

    Read More

  5. Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form

    Jul 15, 24 03:17 PM

    Worksheet on Reducing Fraction
    Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term.

    Read More

Terms of an Algebraic Expression - Worksheet

Worksheet on Types of Algebraic Expressions

Worksheet on Degree of a Polynomial

Worksheet on Addition of Polynomials

Worksheet on Subtraction of Polynomials

Worksheet on Addition and Subtraction of Polynomials

Worksheet on Adding and Subtracting Polynomials

Worksheet on Multiplying Monomials

Worksheet on Multiplying Monomial and Binomial

Worksheet on Multiplying Monomial and Polynomial

Worksheet on Multiplying Binomials

Worksheet on Dividing Monomials