Degree of a Polynomial

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Degree of polynomial is the highest power or degree of the terms, when the polynomial is expressed in terms of the linear combination of the monomials.  To understand the above definition in more clear way, it is important to understand the meaning of degree of term. By the degree of term, we mean the sum of all exponents of the variables involved in the polynomial expression.

The below mentioned following examples will clarify the meaning of degree of polynomial in better way. The examples are as follows.

Example1: Find the degree of the polynomial 6x^2y^3 + 2y^2 + 5

Solution: Given Polynomial 6x^2y^3 + 2y^2 + 5 = 0 has three terms
The first term has a degree of 5 (the sum of 2 and 3 that is 5)
The second term has a degree of 2.
Since the third term does not have any variable so the degree of the term is 0.
Therefore the degree of above polynomial is 5, which is the degree of highest term.
 
Example 2: Verify the degree of the polynomial 5x^3y^3 + 2y^3 + 6 is 6.

Solution: Given Polynomial 5x^3y^3 + 2y^3 + 6has three terms
The first term has a degree of 6 (the sum of 3 and 3 that is 6)
The second term has a degree of 3.
Since the third term does not have any variable so the degree of the term is 0.
As the degree of highest term are 6, therefore by definition the degree of the polynomial 5x^3y^3 + 2y^3 + 6 is 6. Hence verified.

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