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  "body": "\n## Definition\n\nLet $R$ be a [[unique factorisation domain|06YMXJMXYS]] and let $f = a_0 + a_1 x + \\dots + a_n x^n \\in R[x]$.\nThe content of $f$, written $c(f)$, is a [[greatest common divisor|0F7KNJ1ZYN]] of the coefficients $a_0, a_1, \\dots, a_n$.\n\n## Remarks\n\nThe content is unique up to associates. Over $\\mathbb{Z}$, one often takes the positive gcd, with the sign of the leading coefficient in the primitive part.\nFor $f = 6x^2 + 4x - 2$ in $\\mathbb{Z}[x]$, $c(f) = 2$.\nEach nonzero $f$ is $c(f) \\cdot g$ with $g$ a [[primitive polynomial|0SP14DZN0G]], the primitive part of $f$.\nThe content is multiplicative up to units: $c(f g) \\sim c(f) c(g)$. This is a form of [[Gauss's lemma|0QFV5Y1Z5X]].\n\n## Explanations\n\n### L1 human\n\nThe content is the largest common factor that you can pull out of all the coefficients.\nFor $6x^2 + 4x - 2$, you can pull out $2$ and get $2(3x^2 + 2x - 1)$.\n",
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