Polynomial function

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Polynomial function

A polynomial function [math]P\,[/math] is one defined for all real [math]x\,[/math] by an equation on the form

[math]P(x)=c_0+c_1x+\cdots+c_nx^n=\sum_{k=0}^n c_kx^k\,[/math]

the numbers [math]c_0, c_1, \cdots, c_n\,[/math] are called the coefficient of the polynomial, and the nonegative integer [math]n\,[/math] is called its degree if [math]c_n\neq0\,[/math]. 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.


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