Class 9 - What is a Polynomial’s Degree

The degree of a polynomial is the highest power of the variable in a polynomial expression. A polynomial is an expression with more than two algebraic terms, specifically the sum or difference of several terms that have different powers of the same or different variables. It is a combination of monomials. For example, 6x⁴ + 2x³ + 3. 

Table of Contents

• What is the Degree of a Polynomial?
• Degree of Zero Polynomial
• Degree of Constant Polynomial
• How to Find a Degree?

What is the Degree of a Polynomial? 

A polynomial's degree is the highest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial, without considering the coefficients. For example, in 8x⁴ + 2x³ + 5, the terms are 8x⁴, 2x³, and 5. Here, 8x⁴ is the leading term, and 5 is a constant term. The coefficients of the polynomial are 8 and 2. Therefore, the degree of the polynomial 8x⁴ + 2x³ + 5 is 4.

Degree of a Zero Polynomial

A zero polynomial has all coefficients equal to zero. Thus, the degree of a zero polynomial is either undefined or set to -1.

Degree of a Constant Polynomial

A constant polynomial has a value that stays the same. It does not contain variables. For example, P(x) = c. Since there is no exponent, there is no power. Thus, the power of a constant polynomial is zero. Any constant can be written with a variable raised to the power of zero. For example, the constant term 6 can be expressed as P(x) = 6x⁰. 

How to Find the Degree of a Polynomial? 

A polynomial combines variables assigned with exponential powers and coefficients. To find the degree of a polynomial, follow these steps:
For example, for the expression: 3x⁵ + 6x³ + 2x⁵ + 2x² + 5 + 8x + 4. 

Step 1: Combine all like terms, which are the terms with the variable. (3x⁵ + 2x⁵) + 6x³ + 2x² + 8x + (5 + 4). 

Step 2: Ignore all the coefficients. x⁵ + x³ + x² + x + x⁰. 

Step 3: Arrange the variables in descending order of their powers. x⁵ + x³ + x² + x + x⁰. 

Step 4: The largest power of the variable is the degree of the polynomial. deg(x⁵ + x³ + x² + x + x⁰) = 5.