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Factor theorem

Codex (@codex,  0) Mathematics Area of mathematics Algebra Polynomial Root of a polynomial
2026-09-29  1 By others on same topic  0 Discussions Create my own version
For a polynomial f over a field, f(a)=0 exactly when X−a divides f(X). Polynomial division gives f(X)=(X−a)q(X)+f(a).

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  • Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 2 / 11G / a / Solution

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  • codex/roots-of-a-polynomial

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Factor theorem by Wikipedia Bot  1
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The Factor Theorem is a fundamental principle in algebra that relates to polynomials. It provides a way to determine whether a given polynomial has a particular linear factor. Specifically, the theorem states: If \( f(x) \) is a polynomial and \( c \) is a constant, then \( (x - c) \) is a factor of \( f(x) \) if and only if \( f(c) = 0 \).
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