Various'''Polynomial techniques havefactorizaiton''' beentypically developedrefers to [[factor]]ing a [[polynomialspolynomial]]. into From[[irreducible polynomial]]s over a theoreticalgiven [[field]]. Other perspectivefactorizations, such as [[squarefree polynomial|squarefree]] factorization exist, but the problemirreducible canfactorization, bethe regardedmost ascommon, completelyis solvedthe bysubject meansof this article. The factorization depends strongly on the choice of field. For example, the [[fundamental theorem of algebra]], which states that all polynomials with [[complex number|complex]] coefficients have complex roots, i.e,implies theythat a polnomial with [[integer]] [[coefficient]]s can be completely factoredreduced to [[linear function|linear factor]]s over the complex field '''C'''. On the other hand, such a polynomial can may only be reducable to linear and [[quadratic function|quadratic]] factors over the [[real number|real]] field '''R'''. Over the [[rational number]] field '''Q''', it is possible that no factorization at all may be possible. From a more practical vantage point, the fundamental theorem is only an existance proof that offers little insight into the common problem of actually finding the roots of a given polynomial.
