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  "body": "\n## Statement\n\nLet $F$ be a field, let $V$ be a finite-dimensional vector space over $F$, and let $T \\colon V \\to V$ be an endomorphism with [[minimal polynomial|03NDVCSHSB]] $m_T$.\nIf $p \\in F[x]$ and $p(T) = 0$, then $m_T$ divides $p$.\n\n## Remarks\n\nThe proof divides with remainder: $p = q m_T + r$ with $\\deg r \u003c \\deg m_T$.\nThen $r(T) = 0$, so $r = 0$ by the minimality of $\\deg m_T$.\n\n## Explanations\n\n### L1 human\n\nEvery polynomial that kills $T$ is a multiple of the minimal polynomial.\nIf a matrix satisfies $A^2 = A$, then its minimal polynomial divides $x^2 - x$.\nSo it is $x$, $x - 1$ or $x^2 - x$.\n",
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