**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 polynomialp(x) =a+_{n}x^{n}a_{n}_{–1}x^{n}^{–1}+ ··· +a_{2}x^{2}+a_{1}x+a_{0}with degreenat least 1 and with coefficients that may be real or complex must have a factor of the formx–r, wherermay be real or complex.

**See also**

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