Learn Spanish (Spain): No creo que el escándalo mejore su imagen. - I don't believe that the scandal improves her image.

The phrase No creo que denies a belief, which introduces doubt. In Spanish, negative verbs of opinion or thinking like no creer and no pensar trigger the subjunctive in the following clause. That is why we must use mejore.

If I wanted to say 'I believe the scandal improves her image', would I still use mejore?

No, you would use the indicative form mejora. Affirmative statements of belief like creo que or pienso que declare what you consider to be true, so they do not trigger the subjunctive. You only need the subjunctive when the verb of opinion is negative.

Could No creo que also translate to 'I don't think that'?

Yes. In Spanish, creer (to believe) and pensar (to think) are often used interchangeably to express opinions. You will frequently hear native speakers use No creo que exactly where an English speaker would say 'I don't think that'.

The translation says 'her image', but couldn't su also mean his or their?

Absolutely. The possessive adjective su is very flexible and can mean his, her, its, your (formal), or their. Without wider context, this sentence could just as easily translate to 'his image' or 'their image'. If a speaker needs to be completely specific to avoid confusion, they might replace su with la imagen de ella.