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  "body": "\n## Summary\n\nA real polynomial function is a function $\\R \\to \\R$ given by a formula $a_0 + a_1 x + \\dots + a_n x^n$ with real coefficients.\nPolynomial functions are [[continuous|0C5TP6RYSV]] and infinitely differentiable, and their derivatives and antiderivatives are again polynomial functions.\nThey are the simplest functions beyond linear ones, and by the [[Weierstrass approximation theorem|0JQE130DHW]] they approximate every continuous function on a closed bounded interval uniformly.\nThe [[definition|MAM9H3SY3Y]] gives the precise form, and the algebraic side is the [[polynomial ring|0SDC934R52]].\n\n## Explanations\n\n### L1 human\n\nA polynomial function is built from $x$ and constants using only addition and multiplication.\nIts graph is smooth with no corners or jumps.\nA polynomial function of degree $n \\ge 1$ crosses each horizontal line at most $n$ times.\nFor example $f(x) = x^3 - 2x + 1$ has degree $3$ and $f(1) = 0$.\n",
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