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  "body": "\n## Definition\n\nLet $R$ be a [[ring|0894J980RK]].\nA polynomial $f \\in R[x]$ is monic if its [[leading coefficient|0P05RJC5XA]] is $1$.\n\n## Remarks\n\nThe polynomial $x^2 - 2$ is monic, and $2x^2 - 1$ is not.\nIn a nonzero ring, a monic polynomial is not zero.\nThe product of two monic polynomials is monic, over every commutative ring.\nOver a field, each nonzero polynomial is a constant times exactly one monic polynomial.\n\n## Explanations\n\n### L1 human\n\nA monic polynomial starts with $x^d$, with no number in front.\nOver a field, you can make any nonzero polynomial monic by dividing by its leading coefficient.\n",
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