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 Fundamental Theorem of Algebra The theorem that establishes that, using complex numbers, all polynomials can be factored. A generalization of the theorem asserts that any polynomial of degree n has exactly n zeros, counting multiplicity.   Fundamental Theorem of Algebra: A polynomial p(x) = anxn + an–1xn–1 + ··· + a2x2 + a1x + a0 with degree n at least 1 and with coefficients that may be real or complex must have a factor of the form x – r, where r may be real or complex.     See also