Which string matches the regular expression r(ege)+x?

rx contains no 'ege' group at all, but the + quantifier requires at least one occurrence of the group, so rx cannot match.

The regex r(ege)+x matches 'r', then one or more occurrences of the capturing group 'ege', then 'x'. The string 'regeegex' decomposes as r + ege + ege + x - the substring 'egeege' is exactly two back-to-back occurrences of 'ege', satisfying the (ege)+ requirement and producing a valid full match.

r(ege)x contains literal parenthesis characters, which are not present in the regex pattern where parentheses serve as grouping metacharacters rather than literals.

rege+x is a different regex where + applies only to the single character 'e', not to the group 'ege', so it is a distinct pattern and not a valid match for r(ege)+x.