Politiet undersøker saken.

Because Norwegian usually puts the definite article at the end of the noun instead of using a separate word like the.

• politi = police / a police force
• politiet = the police

Here, -et is the definite ending. So politiet already includes the meaning of the.

Grammatically, politiet is usually treated as a singular neuter noun in Norwegian, even though in English the police often feels plural.

So Norwegian says:

• Politiet undersøker saken.

Even though English would often think of the police as a group, Norwegian commonly treats politiet as one collective unit.

Undersøker is the present tense of the verb å undersøke, which means to investigate, to examine, or to look into.

So:

• å undersøke = to investigate
• undersøker = investigates / is investigating

A very common present-tense pattern in Bokmål is:

• infinitive: å undersøke
• present: undersøker

It can mean both, depending on context.

Norwegian does not use the progressive form as often as English does. So:

• Politiet undersøker saken can mean
  
  • The police investigate the case
  • The police are investigating the case

In most real situations, the intended meaning is clear from context.

For the same reason as politiet ends in -et: Norwegian often marks definiteness by adding an ending to the noun.

• sak = case / matter / issue
• saken = the case / the matter

Here, -en is the definite ending for a common-gender noun.

So both nouns in the sentence are definite:

• politiet = the police
• saken = the case

Sak is a broad word that can mean:

• case
• matter
• issue
• affair

In this sentence, because the subject is the police, saken most naturally means the case.

So the sentence suggests that the police are looking into some specific case or matter.

This is the normal basic word order for a main clause in Norwegian:

subject + verb + object

So:

• Politiet = subject
• undersøker = verb
• saken = object

This is very similar to English:

• The police investigate the case

Norwegian main clauses also follow the V2 rule, which means the verb is usually in the second position. In this sentence, the subject comes first, so the order looks straightforward.

For example:

• I dag undersøker politiet saken.
  Today, the police are investigating the case.

Here, undersøker still stays in second position.

Because Norwegian usually uses a suffix instead of a separate article in sentences like this.

Compare:

• English: the police, the case
• Norwegian: politiet, saken

So you should not add an extra the-word before them here. The definiteness is already built into the noun itself.

No. It is capitalized here simply because it is the first word of the sentence.

In Norwegian, common nouns are not normally capitalized just because they refer to institutions.

So in the middle of a sentence, you would usually write:

• Jeg tror politiet undersøker saken.

Only proper names and sentence-initial words get capitals in normal writing.

A rough English-friendly guide is:

• Politiet ≈ poo-lee-TEE-et
• undersøker ≈ UN-der-suh-ker
• saken ≈ SAH-ken

A few useful notes:

• tj / ti in politiet is not like English sh here; it is part of the final syllables -ti-et
• ø is a vowel sound English does not really have, so undersøker may take some practice
• the stress is roughly on:
  • poliTIet
  • UNdersøker
  • SAken

Yes. Å undersøke is fairly broad. Depending on context, it can mean:

• investigate
• examine
• look into

So Politiet undersøker saken could also be understood as:

• The police are looking into the case
• The police are examining the matter

If the context is clearly criminal or legal, investigating the case is the most natural translation.