Definition: Polynomials

Definition 1: Gilbert, J. (1991). Guide to Mathematical Methods. Hampshire, England: Macmillan. (p. 8)

The general polynomial of degree n in x may be written as

    \[y=f\left(x\right)=a_n x^n +a_{n-1} x^{n-1} + \cdots +a_1 n+ a_0\]

where a_0, a_1, \mathellipsis, a_n are numbers and a_n \neq 0.  The degree of a polynomial is simply the highest power of x occurring.  Polynomials are probably the most useful functions in mathematics.  This is because they are so easy to manipulate and compute the values of.

Examples of polynomials:

Polynomial of degree 1: f\left(x\right)=5x+1

Polynomial of degree 3: f\left(x\right)=2x^3-3x+4

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

Leave a Reply