Editing Polynomial (section)

=== Factoring ===
All polynomials with coefficients in a [[unique factorization domain]] (for example, the integers or a [[field (mathematics)|field]]) also have a factored form in which the polynomial is written as a product of [[irreducible polynomial]]s and a constant. This factored form is unique up to the order of the factors and their multiplication by an invertible constant. In the case of the field of [[complex number]]s, the irreducible factors are linear. Over the [[real number]]s, they have the degree either one or two. Over the integers and the [[rational number]]s the irreducible factors may have any degree.<ref name=Barbeau-2003-pp80-82>{{harvnb|Barbeau|2003|pp=[https://books.google.com/books?id=CynRMm5qTmQC&pg=PA80 80]–2}}</ref> For example, the factored form of
<math display="block"> 5x^3-5</math>
is
<math display="block">5(x - 1)\left(x^2 + x + 1\right)</math>
over the integers and the reals, and
<math display="block"> 5(x - 1)\left(x + \frac{1 + i\sqrt{3}}{2}\right)\left(x + \frac{1 - i\sqrt{3}}{2}\right)</math>
over the complex numbers.

The computation of the factored form, called ''factorization'' is, in general, too difficult to be done by hand-written computation. However, efficient [[factorization of polynomials|polynomial factorization]] [[algorithm]]s are available in most [[computer algebra system]]s.