Rational root theorem are found, they can be factored out of the polynomial, resulting in a polynomial of lower degree whose roots are also roots of the original polynomial. The general cubic equation with integer coefficients has three solutions in the complex plane. If it is found by the rational root test that there are no rational solutions, then the only way to express the solutions algebraically is to use cube roots. But if the test finds three rational solutions, then the cube roots are avoided. And if precisely one rational solution "r" is found to exist, then ("x" – "r") can be
Cube root be −2, , or . This is related with the concept of monodromy: if one follows by continuity the function "cube root" along a closed path around zero, after a turn the value of the cube root is multiplied (or divided) by formula_10 Cube roots arise in the problem of finding an angle whose measure is one third that of a given angle (angle trisection) and in the problem of finding the edge of a cube whose volume is twice that of a cube with a given edge (doubling the cube). In 1837 Pierre Wantzel proved that neither of these