A Concrete Introduction to Higher Algebra pp 307-338 | Cite as

# The Fundamental Theorem of Algebra

In Chapter 14 we showed that every nonconstant polynomial in *F*[*x*], *F* a field, factors uniquely (up to associates and the order of the factors) into the product of irreducible polynomials. Irreducible polynomials therefore relate to all polynomials in the same way that primes do to all natural numbers. Thus one naturally asks: Which polynomials are irreducible? and, How does one factor a given polynomial into a product of irreducible polynomials?

When looking for irreducible polynomials over a field, we can restrict our attention to monic polynomials. Every polynomial is an associate of a monic polynomial.

## Keywords

Rational Function Normal Form Real Root Fundamental Theorem Partial Fraction## Preview

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