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  "body": "\n## Definition\n\nLet $L$ be a [[field|0QA8CHH8MG]] and let $f \\in L[x]$ be nonzero.\nThe polynomial $f$ splits over $L$ if there are $c, a_1, \\dots, a_n \\in L$ with\n$$f = c \\, (x - a_1)(x - a_2) \\cdots (x - a_n).$$\n\n## Remarks\n\nThen $c$ is the leading coefficient of $f$, $n = \\deg f$, and $a_1, \\dots, a_n$ are the [[roots|00EHX6FWC0]] of $f$, not necessarily distinct.\nThe polynomial $x^2 - 2$ splits over $\\mathbb{R}$, but not over $\\mathbb{Q}$.\nThe polynomial $x^2 + 1$ splits over $\\mathbb{C}$, but not over $\\mathbb{R}$.\nOver an [[algebraically closed field|02SJG1HC32]], every nonzero polynomial splits.\n\n## Explanations\n\n### L1 human\n\nA polynomial splits when you can factor it completely into linear factors.\nThen you can read all its roots from the factors.\n",
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