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 a polynomial?

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

Examples of polynomials and its degree**:**

We observe that the above polynomial has three terms. Here the first term is 2x

Now we will determine the exponent of each term.

(i) the exponent of the first term 2x

(ii) the exponent of the second term 3x

(iii) the exponent of the third term 5x

Since, the greatest exponent is 6, the degree of 2x

Therefore, the degree of the polynomial 2x

We observe that the above polynomial has five terms. Here the first term is 16, the second term is 8x, the third term is – 12x

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 – 12x

(iv) the exponent of the fourth term 15x

(v) the exponent of the fifth term - x

Since, the greatest exponent is 4, the degree of 16 + 8x – 12x

Therefore, the degree of the polynomial 16 + 8x – 12x

**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.

We observe that the above polynomial has three terms. Here the first term is 11x

Now we will determine the exponent of each term.

(i) the exponent of the first term 11x

(ii) the exponent of the second term - 13x

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

Since, the greatest exponent is 5, the degree of 11x

Therefore, the degree of the polynomial 11x

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

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 x

(iv) the exponent of the fourth term x

Since, the greatest exponent is 3, the degree of 1 + x + x

Therefore, the degree of the polynomial 1 + x + x

**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

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

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**● ****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

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