How to Find the Degree of a Polynomial?

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 + 7x3 + 2x5+ 3x2+ 5 + 8x + 4

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

(5x5 + 2x5) + 7x3 + 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 Polynomial

Degree of a Polynomial Importance

To find whether the given polynomial expression is homogeneous or not, the degree of the terms in the polynomial plays an important role. The homogeneity of polynomial expression can be found by evaluating the degree of each term of the polynomial. For example, 3x3 + 2xy2+4y3 is a multivariable polynomial. To check whether the polynomial expression is homogeneous, determine the degree of each term. If all the degrees of the term are equal, then the polynomial expression is homogeneous. If the degrees are not equal, then the expression is non-homogenous. From the above given example, the degree of all the terms is 3. Hence, the given example is a homogeneous polynomial of degree 3.