Degree of a Polynomial

Identify the highest power of the variable in a polynomial expression.

Input Expression

Polynomial p(x)

Visual Guide

P(x) = 3x^4 + ... + - 5

The highest power of x identifies the degree of the polynomial.

Polynomial Analysis

Degree (n)

Leading Term3x^4

Leading Coefficient3

Constant Term- 5

What is the Degree?

The degree of a polynomial is the highest exponential power of its variable. For multi-variable polynomials, it is the highest sum of exponents in any single term. The degree determines the maximum number of real roots the polynomial can have and its end behavior.

💡

Pro Tips

A constant (like '5') has degree 0.
The degree of the zero polynomial is undefined (or -1 in some contexts).
Linear polynomials have degree 1, quadratics have degree 2, and cubics have degree 3.

Fun Facts

"The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n complex roots."
"Polynomial degrees are used in computer science to describe the time complexity of algorithms."
"The 'Abel-Ruffini Theorem' proves there is no general formula for roots of polynomials of degree 5 or higher."

Formula: P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₀

Used with this

Similar tools that might be useful

Abi Form

Aaa Triangle

Aas Triangle