Have you unlocked the lesson about adjectives? If you have you should read the tips and notes section.
It's only "rød" if the adjective is the predicative (and the noun it tells you something about is either masculine or feminine) or if it is attributive to an indefinite noun (masculine or feminine).
Here it is an attributive adjective, and attributive adjectives that describe definite nouns take the ending -e(inflection), just like attributive adjectives that describe a plural noun.
Are you asking whether it's grammatically correct? If so, yes it is.
When dealing with definite singular nouns, the attributive adjectives (the ones placed before the noun) take the definite version of the adjective, while the predicative adjectives (the ones placed after the noun and verb) take the indefinite singular form.
den røde genseren (attributive adjective placement)
genseren er rød (predicative adjective placement)
This is all a little confusing, but from your sentence it seems like you've already worked it out! :)
a quick question: how would you say 'this red sweather is mine'? Would it be 'denne rød genseren er min'? Or is it 'denne røde genseren'? Also, would this Norwegian sentence translate to "that red sweater is mine" or should this rather be "den rød genseren er min"? The reason I'm asking is because the (normal speed) audio got me very confused and it also got me thinking how it should be. Tusen takk :)
It’s “røde” in both cases: “den røde genseren” and “denne røde genseren”.
When written the sentence is ambiguous and can mean both “the red sweater is mine” and “that red sweater is mine”. However, they are pronounced differently. If you want to say “that red sweater is mine”, you must emphasise “den”.