Degree of polynomial explained with example

Learn how to find the degree of polynomial. This is a simple concept in algebra so everyone can understand what is the degree of polynomial.

Degree of polynomial explained with example

Before discussing about degree first we will see what is mean by polynomial. An expression which contains one or more terms is considered as a polynomial. After this now we will learn what is the meaning of degree of a polynomial and how to find it.

Definition of degree of polynomial:

The highest power of the term in the given polynomial is called as the degree of polynomial.

Example:

3 { x }^{ 3 } + 5 { x }^{ 7 } – 9 { x }^{ 2 } in this polynomial the degree is “7”.

Explanation:

In 3 { x }^{ 3 } + 5 { x }^{ 7 } – 9 { x }^{ 2 } we have three terms. First term variable power is 3 and second term variable power is 7 finally third term variable power is 2. So in all these which is highest power means it is 7. Therefore the degree of polynomial 3 { x }^{ 3 } + 5 { x }^{ 7 } – 9 { x }^{ 2 } is “7”.

17 { y }^{ 12 } – 24 { y }^{ 8 } + { y }^{ 14 } – 71 { y }^{ 37 } in this polynomial the degree is 37.

Explanation:

For this polynomial also the process will be same as first example. We have four terms. First term variable power is 12, second term variable power is 8, third term variable power is 14 and fourth term variable power is 37. The highest power is 37. So the degree of polynomial 17 { y }^{ 12 } – 24 { y }^{ 8 } + { y }^{ 14 } – 71 { y }^{ 37 } is 37.

23 { x }^{ 2 } { y }^{ 3 } + 54 { x }^{ 2 } { y }^{ 4 } – 37 { x }^{ 2 } { y }^{ 2 } in this polynomial the degree is “6”.

Explanation:

The polynomial contains four terms.

First term variables power sum is (2+3)=5.

Second term variables power sum is (2 + 4) =6.

Third term variables power sum is (2 + 2) =4

In all the three the highest power is 6.

So the degree of polynomial 23 { x }^{ 2 } { y }^{ 3 } + 54 { x }^{ 2 } { y }^{ 4 } – 37 { x }^{ 2 } { y }^{ 2 } is “6”.

Hope I gave enough examples and explanation for finding degree of polynomial.

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