Definition:Polynomial/Real Numbers
< Definition:Polynomial(Redirected from Definition:Polynomial over Real Numbers)
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Definition
A polynomial (in $\R$) is an expression of the form:
- $\ds \map P x = \sum_{j \mathop = 0}^n \paren {a_j x^j} = a_0 + a_1 x + a_2 x^2 + \cdots + a_{n - 1} x^{n - 1} + a_n x^n$
where:
- $x \in \R$
- $a_0, \ldots a_n \in \mathbb k$ where $\mathbb k$ is one of the standard number sets $\Z, \Q, \R$.
Examples
Arbitrary Example
The polynomial:
- $x^3 - 2 x + 6$
is of degree $3$.
Also see
- Results about polynomial theory can be found here.
Sources
- 1960: Margaret M. Gow: A Course in Pure Mathematics ... (next): Chapter $1$: Polynomials; The Remainder and Factor Theorems; Undetermined Coefficients; Partial Fractions: $1.1$. Polynomials in one variable
- 1973: G. Stephenson: Mathematical Methods for Science Students (2nd ed.) ... (previous) ... (next): Chapter $1$: Real Numbers and Functions of a Real Variable: $1.3$ Functions of a Real Variable: $\text {(d)}$ Polynomials $(4)$
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 64$. Polynomial rings over an integral domain
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): polynomial