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  "body": "\n## Definition\n\nLet $R$ be a [[commutative ring|0GYGHKX834]].\nA polynomial $f \\in R[x]$ is primitive if every $r \\in R$ that divides $f$ in $R[x]$ is a unit.\nHere $r$ divides $f$ when $r$ divides each coefficient of $f$.\n\n## Remarks\n\nIf $R$ is a [[unique factorisation domain|06YMXJMXYS]], then $f$ is primitive if and only if its [[content|08VV7YJRB7]] is a unit.\nIn $\\mathbb{Z}[x]$, $3x^2 + 2x - 1$ is primitive and $6x^2 + 4x - 2$ is not.\nEvery [[monic polynomial|0BDX4MBKT4]] is primitive.\nThe word primitive polynomial has another meaning over a finite field: a polynomial whose root is a [[primitive element|0YAA9CJQXF]].\n\n## Explanations\n\n### L1 human\n\nA primitive polynomial has coefficients with no common factor.\nOver the integers, this means that the gcd of the coefficients is $1$.\n",
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