As with integers, operations related to division are key to many computations with polynomials. Mathematica includes not only highly optimized univariate polynomial-division ...

Counting roots of polynomials. CountRoots accepts polynomials with Gaussian rational coefficients. The root count includes multiplicities. This gives the number of real roots ...

NSolve gives you a general way to find numerical approximations to the solutions of polynomial equations. Finding numerical solutions to more general equations, however, can ...

SymmetricPolynomial[k, {x_1, ..., x_n}] gives the k\[Null]^th elementary symmetric polynomial in the variables x_1, ..., x_n.

$RootDirectory gives the root directory of your file system.

RootOfUnityQ[a] yields True if a is a root of unity, and yields False otherwise.

The leading term of a polynomial can be chosen in many different ways. For multivariate polynomials, sorting by the total degree of the monomials is often useful. Different ...

InterpolatingPolynomial[{f_1, f_2, ...}, x] constructs an interpolating polynomial in x which reproduces the function values f_i at successive integer values 1, 2, ... of x. ...

PolynomialQuotient[p, q, x] gives the quotient of p and q, treated as polynomials in x, with any remainder dropped.

PolynomialMod[poly, m] gives the polynomial poly reduced modulo m. PolynomialMod[poly, {m_1, m_2, ...}] reduces modulo all of the m_i.