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  "body": "\n## Summary\n\nPolynomial long division is the algorithm that divides a polynomial $f$ by a polynomial $g$ with invertible leading coefficient.\nIt produces the quotient $q$ and the remainder $r$ with $f = q g + r$ and $\\deg r \u003c \\deg g$.\nThese are the quotient and remainder of the [[division algorithm for polynomials|0MES3KS0ZC]].\nIt is the basic step of the [[Euclidean algorithm|023VY493K0]] for polynomials and of many computations in algebra.\n\n## Explanations\n\n### L1 human\n\nIt works like long division of integers, with degrees in place of digits.\nAt each step you divide the leading term of what is left by the leading term of $g$.\nYou write this term in the quotient, subtract its product with $g$, and go on.\nFor example, dividing $x^2 + 1$ by $x - 1$ gives the quotient $x + 1$ and the remainder $2$, since $x^2 + 1 = (x + 1)(x - 1) + 2$.\nThe [[definition|FTAK2F0TR3]] gives the steps.\n",
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