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 a 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.

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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