Fix doctests

and put these factorizations in here that look much nicer/make much more sense.

Author: saraedum

src/sage/rings/fraction_field.py

@@ -864,7 +864,7 @@ def _factor_univariate_polynomial(self, f):
             sage: R.<x> = K[]
             sage: f = x^3 + a
             sage: f.factor()
-            (t + 2*a + 1)^3
+            (x + 2*a + 1)^3
 
         """
         # The default implementation would try to convert this element to singular and factor there.

src/sage/rings/polynomial/polynomial_element.pyx

@@ -3993,9 +3993,9 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: factor(x)
             x
             sage: factor(x^2 - q^2)
-            (-1) * (-x + q) * (x + q)
+            (x - q) * (x + q)
             sage: factor(x^2 - q^-2)
-            (1/q^2) * (q*x - 1) * (q*x + 1)
+            (x - 1/q) * (x + 1/q)
 
             sage: P.<a,b,c> = PolynomialRing(ZZ)
             sage: R.<x> = PolynomialRing(FractionField(P))