Polynomial function

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Definition
 Polynomial function A polynomial function $P\,$ is one defined for all real $x\,$ by an equation on the form $P(x)=c_0+c_1x+\cdots+c_nx^n=\sum_{k=0}^n c_kx^k\,$ the numbers $c_0, c_1, \cdots, c_n\,$ are called the coefficient of the polynomial, and the nonegative integer $n\,$ is called its degree if $c_n\neq0\,$. They include the constant functions and the power functions as special cases. Polynomials of degree 2, 3 and 4 are called quadratic, cubic, and quartic polynomials, respectively.

Examples

$\text{Polynomial function }\,$$P(x)=\frac{1}{2}x^4+3x^2\,$
$x\,$ $P(x)\,$
$-5\,$ $387.5\,$
$-4\,$ $176.0\,$
$-3\,$ $67.5\,$
$-2\,$ $20.0\,$
$-1\,$ $3.5\,$
$0\,$ $0.0\,$
$1\,$ $3.5\,$
$2\,$ $20.0\,$
$3\,$ $67.5\,$
$4\,$ $176.0\,$
$5\,$ $387.5\,$