Factor a polynomial

Factor[x ^ 3 - 3x ^ 2 - 2x + 6]

(-3 + x)*(-2 + x^2)

Factor[x ^ 3 - 3x ^ 2 - 2x + 6, Extension -> Sqrt[2]]

Factor[6 - 2*x - 3*x^2 + x^3, Extension -> Sqrt[2]]

Factor[x ^ 3 - 3x ^ 2 - 2x + 6, Modulus -> 3]

x*(1 + x^2)

Factor[x ^ 3y ^ 2 - 3x ^ 2y - 2x y ^ 3 + 6y ^ 2]

-(y*(-x^2 + 2*y)*(-3 + x*y))

IrreduciblePolynomialQ[x ^ 2 + x + 1]

True

PolynomialGCD[x ^ 2 - 1, x ^ 2 + 2x + 1, x ^ 3 - x ^ 2 - x + 1]

1 + x

Roots[x ^ 3 - 3x ^ 2 - 2x + 6 == 0, x]

x == -Sqrt[2] || x == Sqrt[2] || x == 3