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  "body": "\n## Definition\n\nLet $R$ be a [[ring|0894J980RK]] and let $f = a_0 + a_1 x + \\dots + a_n x^n$ be a nonzero polynomial in $R[x]$ of [[degree|0DPF6WRZW6]] $d$.\nThe leading coefficient of $f$ is $a_d$.\nThe leading coefficient of the zero polynomial is $0$.\n\n## Remarks\n\nThe leading coefficient of $3x^4 - x + 2$ is $3$.\nA polynomial with leading coefficient $1$ is [[monic|0BDX4MBKT4]].\nIn an [[integral domain|09S3PFBEPM]], the leading coefficient of $f g$ is the product of the leading coefficients of $f$ and $g$.\n\n## Explanations\n\n### L1 human\n\nThe leading coefficient is the number in front of the highest power of $x$.\nFor large values of $x$, the leading term $a_d x^d$ decides the size of a real polynomial.\n",
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