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  "body": "\n## Summary\n\nHorner's method evaluates a polynomial of degree $n$ with $n$ multiplications and $n$ additions.\nIt rewrites $a_n x^n + \\dots + a_0$ as a nested product $a_0 + x(a_1 + x(a_2 + \\dots + x a_n))$.\nThe intermediate values are the coefficients of the quotient by $x - c$, so it also performs synthetic division.\nIt is the standard way to carry out [[polynomial evaluation|02MAKWDKGT]].\n\n## Explanations\n\n### L1 human\n\nTo compute $2x^3 - 6x^2 + 2x - 1$ at $x = 3$, you do not need the powers of $3$.\nStart with $2$; multiply by $3$ and add $-6$ to get $0$; multiply by $3$ and add $2$ to get $2$; multiply by $3$ and add $-1$ to get $5$.\nSo the value is $5$.\nEach step is one multiplication and one addition.\nThe [[definition|Z2EWA10YMB]] gives the recursion.\n",
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