Degree of a Polynomial

The degree of a polynomial is the highest degree in a polynomial expression. To recall, a polynomial is defined as an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). It is a linear combination of monomials. For Example: 6x4 + 2x3+ 3

What is the Degree of a Polynomial?

A polynomial’s degree is the highest or the greatest degree of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients).

For Example: 6x4 + 2x3+ 3

The degree of the polynomial 6x4 + 2x3+ 3 is 4.

Let’s take another example: 3x8+ 4x3 + 9x + 1

The degree of the polynomial 3x8+ 4x3 + 9x + 1 is 8.

Degree of a Zero Polynomial

A zero polynomial is the one where all the coefficients are equal to zero. So, the degree of the zero polynomial is either undefined, or it is set equal to -1.

Degree of a Constant Polynomial

A constant polynomial is that whose value remains the same. It contains no variables. The example for this is: P(x)=c. Since there is no exponent so no power to it. Thus, the power of the constant polynomial is Zero. Any constant can be written with a variable with the exponential power of zero. Constant term = 6 Polynomial form P(x)= 6x0

How to Find the Degree of a Polynomial?

A Polynomial is merging of variables assigned with exponential powers and coefficients. The steps to find the degree of a polynomial are as follows:- For example if the expression is :5x5 + 7 x3 + 2x5+ 3x2+ 5+ 8x + 4

  • Step 1: Combine all the like terms that are the terms with the variable terms.

(5x5+ 2x5) + 7 x3+ 3x2+ 8x + (5 +4)

  • Step 2: Ignore all the coefficients

x5+ x3+ x2+ x1 + x0

  • Step 3: Arrange the variable in descending order of their powers

x5+ x3+ x2+ x1 + x0

  • Step 4: The largest power of the variable is the degree of the polynomial

deg( x5+ x3+ x2+ x1 + x0) = 5

Types of Polynomials Based on its Degree

Every polynomial with a specific degree has been assigned a specific name as follows:-

Degree Polynomial Name
Degree 0 Constant Polynomial
Degree 1 Linear Polynomial
Degree 2 Quadratic Polynomial
Degree 3 Cubic Polynomial
Degree 4 Quartic Polynomials

Example Questions Using Degree of Polynomials Concept

Some of the examples of the polynomial with its degree are:

  • 5x5+4x2-4x+ 3 – The degree of the polynomial is 5
  • 12x3 -5x2 + 2 – The degree of the polynomial is 3
  • 4x +12 – The degree of the polynomial is 1
  • 6 – The degree of the polynomial is 0

Topics Related to Polynomial Degree

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Frequently Asked Questions

What is the Degree of a Polynomial?

The degree of a polynomial is defined as the highest power of the degrees of its individual terms (i.e. monomials) with non-zero coefficients.

What is the Degree of a Quadratic Polynomial?

A quadratic polynomial is a type of polynomial which has a degree of 2. So, a quadratic polynomial has a degree of 2.

What is a 3rd Degree Polynomial?

A third-degree (or degree 3) polynomial is called a cubic polynomial.

Find the Degree of this Polynomial: 5x5+7x3+2x5+9x2+3+7x+4.

To find the degree of the given polynomial, combine the like terms first and then arrange it in ascending order of its power.

So, 5x5+7x3+2x5+9x2+3+7x+4 = 7x5 + 7x+ 9x+ 7x + 7

Thus, the degre of the polynomial will be 5.

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