Factor

Factor(expr)

factors the polynomial expression expr

Factor(expr, GaussianIntegers->True)

for gaussian integers you can set the option GaussianIntegers->True

Factor(expr, Modulus->p)

to treat integers modulo an integer number p, you can set the option Modulus->p.

See:

>> Factor(1+2*x+x^2, x)
(1+x)^2

>> Factor(x^4-1, GaussianIntegers->True)
(x-1)*(x+1)*(x-I)*(x+I)

>> Factor(x^3 + 3*x^2*y + 3*x*y^2 + y^3)
(x+y)^3

Factor can also be used with equations:

>> Factor(x*a == x*b+x*c)
a*x==(b+c)*x

and lists:

>> Factor({x + x^2, 2*x + 2*y + 2})
{x*(1+x),2*(1+x+y)}