RootReduce[expr] attempts to reduce expr to a single Root object.

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

Mathematica provides many functions to group terms in a polynomial, extract and sort the monomials, display them in various ways, and even process them as arbitrary ...

RootApproximant[x] converts the number x to one of the "simplest" algebraic numbers that approximates it well.RootApproximant[x, n] finds an algebraic number of degree at ...

Roots[lhs == rhs, var] yields a disjunction of equations which represent the roots of a polynomial equation.

NRoots[lhs == rhs, var] yields a disjunction of equations which represent numerical approximations to the roots of a polynomial equation.

IsolatingInterval[a] gives a rational isolating interval for the algebraic number a.IsolatingInterval[a, dx] gives an isolating interval of width at most dx.

CountRoots[poly, x] gives the number of real roots of the polynomial poly in x.CountRoots[poly, {x, a, b}] gives the number of roots between a and b.

Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

RootSum[f, form] represents the sum of form[x] for all x that satisfy the polynomial equation f[x] == 0.