Find degree, leading coefficient, leading term, and constant term
Coefficients from highest degree to constant
Result
Degree
Leading Term
Step-by-Step Derivation
Polynomial Degree Rule
Degree = highest exponent with nonzero coefficient
The degree of a polynomial is determined by the highest power of x that has a nonzero coefficient. Leading zero coefficients do not count, because they do not actually contribute a term to the polynomial. Once the leading nonzero term is found, its exponent becomes the polynomial degree and its coefficient becomes the leading coefficient. These values help classify the polynomial and predict graph behavior.
⚠Note: Coefficients must be entered in descending degree order.
What This Tool Identifies
Polynomial degree describes the largest power of x with a nonzero coefficient. It is one of the first features used to classify a polynomial and understand its behavior.
Leading Term
The highest-degree term after ignoring leading zeros.
Leading Coefficient
The coefficient attached to the leading term.
Constant Term
The final coefficient in the list is the constant term.
Zero Polynomial
If every coefficient is zero, the degree is undefined.
💡 Example: 3,0,-2,5 represents 3x³-2x+5, so the degree is 3 and the leading coefficient is 3.
Applications
Polynomial ClassificationGraph BehaviorDivision
Frequently Asked Questions
What is a polynomial degree calculator?▼
It identifies the highest exponent with a nonzero coefficient and reports the polynomial degree.
What is the leading coefficient?▼
The leading coefficient is the coefficient of the highest-degree nonzero term.
How do I enter coefficients?▼
Enter coefficients from highest degree to constant term, separated by commas.
What is the degree of the zero polynomial?▼
The zero polynomial has no defined degree in standard algebra.
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