factor() issue with second degre polynomes

edit

If p is a simple polynomial with variable x, then sometimes the following (too) simple function can work

def rad_factor(p):
    s=solve(p,x,multiplicities=True)
    z=zip(map(lambda x:x.rhs(),s[0]),s[1])
    return p.leading_coeff(x)*prod([(x-y[0])^y[1] for y in z])

Or using the suggestion by John Palmieri

def rad_factor(p):
    return p.leading_coeff(x)*(prod((x-_[0])^_[1] for _ in p.roots()))

If you don't know the roots, you can use H.roots(). For example:

sage: H=2*(x+5)**2-4
sage: H.roots()
[(-sqrt(2) - 5, 1), (sqrt(2) - 5, 1)]
sage: prod((x-_[0])^_[1] for _ in H.roots())
(x - sqrt(2) + 5)*(x + sqrt(2) + 5)

Note that this has leading coefficient 1, not 2, so it's not equal to H. This could be repaired by multiplying by

sage: H.simplify_full().leading_coefficient(x)
2

sage: R.<x>=PolynomialRing(QQ[sqrt(2)],'x')
sage: R(2*x**2+20*x+46).factor()           
(2) * (x - sqrt2 + 5) * (x + sqrt2 + 5)