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polynomial

An expression built by adding and subtracting whole-number powers of a variable, each multiplied by a fixed number.

A polynomial in $x$ is a sum of terms of the form $a_n x^n$ for whole-number exponents $n \geq 0$ and fixed coefficients $a_n$ , such as $3x^2 - 5x + 7$ . Every polynomial is defined for every real $x$ — no denominator, radical, or other restriction can ever rule out an input.

Examples

$x^3 - 2x + 1$ is a polynomial; $\dfrac{1}{x}$ and $\sqrt{x}$ are not, since neither is a sum of whole-number powers of $x$ .

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