Polynomial: Difference between revisions
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{{#content:Q2150}} | {{#content:Q2150}} | ||
then $P(x)$ is a '''polynomial''' of '''degree''' $n$ over $\mathbb{F}$. $a_n$ is said to be its '''leading coefficient''', and $a_nx^n$ its '''leading term'''. | |||
<blockquote> | <blockquote> | ||
$P(x)=0$ is known as the '''zero polynomial'''. | |||
</blockquote> | </blockquote> | ||
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$x+x^{\frac{1}{2}}$ is '''not''' a polynomial as $\frac{1}{2}\notin \mathbb{N}$ | $x+x^{\frac{1}{2}}$ is '''not''' a polynomial as $\frac{1}{2}\notin \mathbb{N}$ | ||
</blockquote> | </blockquote> | ||
<ref>{{#cite:Q2204}}</ref> | |||
Revision as of 13:27, 16 October 2026
Mathematical definition
Let $P(x)$ be a mathematical function $P:\mathbb{F} \to \mathbb{F}$
If $P(x)$, through algebraic manipulation, can be written in the form of
$$P(x)=\sum_{k=0}^{n} a_k x^k, n\in\mathbb{N},a_0, a_1, \dots, a_n\in \mathbb{F}$$
where $x\in \mathbb{F}$ is an independent variable
then $P(x)$ is a polynomial of degree $n$ over $\mathbb{F}$. $a_n$ is said to be its leading coefficient, and $a_nx^n$ its leading term.
$P(x)=0$ is known as the zero polynomial.
$x+x^{\frac{1}{2}}$ is not a polynomial as $\frac{1}{2}\notin \mathbb{N}$