Editing Factorization (section)

===Using formulas for polynomial roots===
Any univariate [[quadratic polynomial]] <math>ax^2+bx+c</math> can be factored using the [[quadratic formula]]:
:<math>
ax^2 + bx + c = a(x - \alpha)(x - \beta)  = a\left(x - \frac{-b + \sqrt{b^2-4ac}}{2a}\right) \left(x - \frac{-b - \sqrt{b^2-4ac}}{2a}\right),
</math>
where <math>\alpha</math> and <math>\beta</math> are the two [[zero of a function|roots]] of the polynomial.

If {{math|''a, b, c''}} are all [[real number|real]], the factors are real if and only if the [[discriminant]] <math>b^2-4ac</math> is non-negative. Otherwise, the quadratic polynomial cannot be factorized into non-constant real factors.

The quadratic formula is valid when the coefficients belong to any [[Field (mathematics)|field]] of [[Characteristic (algebra)|characteristic]] different from two, and, in particular, for coefficients in a [[finite field]] with an odd number of elements.<ref>In a field of characteristic 2, one has 2 = 0, and the formula produces a division by zero.</ref>

There are also formulas for roots of [[cubic function|cubic]] and [[quartic function|quartic]] polynomials, which are, in general, too complicated for practical use. The [[Abel–Ruffini theorem]] shows that there are no general root formulas in terms of radicals for polynomials of degree five or higher.