polynomial

 

A polynomial is a mathematical expression made up of indeterminates, or variables, and their coefficients using only the operations of addition, subtraction, multiplication, division, and non-negative integer exponentiation.

The form of a single indeterminate, aka univariate, polynomial is:

a_{n}x^n + a_{n-1}x^{x-1} + \cdots + a_{2}x^2 + a_{1}x + a_0

This can be condensed using a summation:

\sum_{i=0}^{n}a_{i}x^{i}

The exponent on an indeterminate is the called indeterminate’s degree.

In multivariate polynomials, polynomials with more than one indeterminate, an individual term’s degree is the sum of its indeterminate’s degrees. (For a univariate polynomial, a tern’s degree is equal to the indeterminate’s degree.)

The degree of the polynomial is the degree of the term with the largest degree and non-zero coefficient.

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