# 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: 6x^{4} + 2x^{3}+ 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:** 6x^{4} + 2x^{3}+ 3

The degree of the polynomial 6x^{4} + 2x^{3}+ 3 is 4.

**Let’s take another example:** 3x^{8}+ 4x^{3} + 9x + 1

The degree of the polynomial 3x^{8}+ 4x^{3} + 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)= 6x^{0}

## 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 :5x^{5} + 7 x^{3} + 2x^{5}+ 3x^{2}+ 5+ 8x + 4

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

(5x^{5}+ 2x^{5}) + 7 x^{3}+ 3x^{2}+ 8x + (5 +4)

**Step 2:**Ignore all the coefficients

x^{5}+ x^{3}+ x^{2}+ x^{1} + x^{0}

**Step 3:**Arrange the variable in descending order of their powers

x^{5}+ x^{3}+ x^{2}+ x^{1} + x^{0}

**Step 4:**The largest power of the variable is the degree of the polynomial

deg( x^{5}+ x^{3}+ x^{2}+ x^{1} + x^{0}) = **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:

- 5x
^{5}+4x^{2}-4x+ 3 – The degree of the polynomial is 5 - 12x
^{3 }-5x^{2}+ 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: 5x^{5}+7x^{3}+2x^{5}+9x^{2}+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, 5x^{5}+7x^{3}+2x^{5}+9x^{2}+3+7x+4 = 7x^{5} + 7x^{3 }+ 9x^{2 }+ 7x + 7

Thus, the degre of the polynomial will be 5.