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Polynomial

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A polynomial is an expression formed from one or more terms and constants by addition, each term of which should contain a variable raised to a non-negative integer power.

Formal Definition

Let R be a ring (such as the real numbers, rational numbers, or integers). Now let n be a natural number and a_0,a_1,\dots,a_n be elements of R. Then the function p:R\rightarrow R defined by:

p\left(x\right)=\sum_{k=0}^{n}a_{k}x^{k}=a_{n}x^{n}+a_{n-1}x^{n-1}+\dots+a_{2}x^{2}+a_{1}x+a_{0}

For all x in R is said to be a polynomial function in a single variable.

Moreover, if a_n\ne 0, we say that p is an nth-degree polynomial.

We denote the set of polynomials as R\left[x\right].

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