Degree Of A Polynomial

By Author: nandan nayak
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You can perform various operations on a polynomial, such as multiplication, division, addition and a lot more. In this article, we will learn about the Degree of a polynomial in detail. In addition, we will have an overview about:
Dividing polynomials
Finding zeros of polynomials

What is the Degree of a Polynomial?
In algebra, “Degree” refers to “Order”. If the polynomial expression has only one variable, then the degree of polynomial is the biggest exponent of this variable. If the polynomial has several variables, then you have to follow certain strategies to find the degree of a polynomial.

How to find the Degree of a Polynomial?
Once you receive a polynomial expression, check for the number of variables in it. If it has only one variable, then finding the degree is easy. Identify the biggest exponent of the variable and that becomes the degree.

For example, consider the polynomial expression: 5x4 + 3x3 + 2x +8
In this expression, there is only one variable called x. Now check for the exponent values of this variable. Exponent of 5x4 is 4, 3x3 is 3 and 2x is 1. ...
... Among the exponent values 4, 3 and 1, the exponent 4 is biggest. Thus, the degree of polynomial 5x4 + 3x3 + 2x +8 is 4.

What if the polynomial has more than one variable? Consider this example: 3x2y2 + 4xy3 + 6x2. This expression has two variables x and y. In such a case, the exponent of each term will be identified by adding the exponents of variables within the term. Now check which term has the biggest exponent and return that value as degree of the polynomial. For example,

Find the degree of each term in 3x2y2 + 4xy3 + 6x2 as shown below:
3x2y2 - Exponent of x is 2 and y is 2. Add them. The degree of this term is 4.
4xy3 – Exponent of x is 1 and y is 3. Add them. The degree of 4xy3 is 4.
6x2 – Exponent of x is 2. The degree of 6x2 is 2.

Now check for the highest degree among the terms, it is 4. Thus, the degree of this polynomial expression is 4.

How to divide Polynomials?
The division can be performed on polynomials through simplification methodology or by using long division. When the denominator or the divisor has only one or two terms, then you can divide polynomials using simplification. If the denominator has 2 or more terms, then the division is performed using long division method.

How to find zeros of polynomials?
If you wanted to solve a complex polynomial expression which has more than 4 terms, then you have to find the zeros of polynomial and then proceed. The zero of polynomial is nothing but an input value, when this input value is plugged into the polynomial it will return the value 0 for the entire polynomial. Finding zeros of polynomials is possible by performing Rational Roots Test followed by Synthetic Division.
Not just these, Polynomials are a wider concept. You have to apply lots of techniques and strategies while solving polynomials.

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