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
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 + 7x3 + 9x2 + 7x + 7
Thus, the degre of the polynomial will be 5.