Quickly divide a polynomial by (x − c) and read off quotient and remainder.
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Why it works
Synthetic division is Horner’s method in disguise: evaluating and dividing by (x − c) uses only the coefficients, because each step “multiply by c, add to next coefficient” mirrors subtracting c times the previous quotient term. The last number is the remainder — which equals P(c) by the Remainder Theorem.
