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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 [[polynomial|0Q9EZS90GY]] in $R[x]$.\nIf $f \\neq 0$, the degree $\\deg f$ of $f$ is the largest integer $d$ with $a_d \\neq 0$.\nThe degree of the zero polynomial is $\\deg 0 = -\\infty$.\n\n## Remarks\n\nThe degree of $3x^4 - x + 2$ in $\\mathbb{Z}[x]$ is $4$. A nonzero constant polynomial has degree $0$.\nSome authors leave $\\deg 0$ undefined, or set it to $-1$. The convention $-\\infty$ makes the formula $\\deg(f g) = \\deg f + \\deg g$ hold also for $f = 0$ or $g = 0$.\nFor all $f, g \\in R[x]$, $\\deg(f + g) \\le \\max(\\deg f, \\deg g)$.\nThe coefficient $a_d$ with $d = \\deg f$ is the [[leading coefficient|0P05RJC5XA]] of $f$.\n\n## Explanations\n\n### L1 human\n\nThe degree is the highest power of $x$ that really appears in the polynomial.\nFor example, $x^3 + 5x$ has degree $3$.\nThe zero polynomial has no nonzero coefficient, so it needs a special convention.\n",
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