Førstebetjenten undersøker saken.

Because Norwegian usually writes compound nouns as a single word.
So første + betjent become førstebetjent.

This is very common in Norwegian. English often uses two words where Norwegian uses one:

• police officer
• train station
• school bus

In Norwegian, equivalent compounds are often written together.

The -en is the definite singular ending, so it works a lot like the in English.

Compare:

• en førstebetjent = a first officer / an officer
• førstebetjenten = the first officer / the officer

Norwegian often adds definiteness to the end of the noun instead of using a separate word before it.

Because Norwegian commonly expresses definiteness with a suffix on the noun.

So:

• førstebetjenten already means the førstebetjent
• saken already means the case

A separate word like den is not normally used here. You usually only get den together with a definite noun when there is an adjective or similar modifier:

• den erfarne førstebetjenten = the experienced officer

The dictionary form is å undersøke, which is the infinitive.

So:

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

The sentence uses the present tense form.

In Bokmål, many verbs form the present tense with -er.

So:

• å undersøke → undersøker

Unlike English, Norwegian does not change the verb depending on the subject:

• jeg undersøker
• du undersøker
• han/hun undersøker
• vi undersøker

The verb form stays the same.

It can often cover both, depending on context.

Norwegian does not use a progressive form as much as English does. So the simple present can be used where English might say either:

• investigates
• is investigating

If Norwegian really wants to emphasize an ongoing action, it can use another construction, such as:

• holder på å undersøke

But in a simple sentence like this, undersøker is completely normal.

Because saken is definite singular: the case.

Compare:

• sak = the basic noun form
• en sak = a case
• saken = the case

So if the meaning is a specific case, saken is the natural form.

This is about noun gender in Bokmål.

Sak is traditionally a feminine noun. In Bokmål, many feminine nouns can be treated in two ways:

• feminine style: ei sak, saka
• common/masculine-style forms: en sak, saken

Both can be correct in Bokmål, depending on style and preference.
So saken is perfectly normal Bokmål.

The sentence has normal main-clause word order:

Subject + Verb + Object

• Førstebetjenten = subject
• undersøker = verb
• saken = object

So it matches English word order quite closely here.

Then Norwegian uses its usual V2 rule: the finite verb still has to be in second position.

So:

• Førstebetjenten undersøker saken.
• I dag undersøker førstebetjenten saken.

Notice that after I dag, the verb undersøker comes immediately, before the subject. That is very typical Norwegian main-clause word order.

Only because it is the first word of the sentence.

Norwegian does not capitalize common nouns the way German does. So in the middle of a sentence, it would normally be:

• førstebetjenten undersøker saken

The letter ø has no exact English equivalent, but a rough approximation is the vowel in British English bird or nurse, with rounded lips.

You hear it in:

• Første-
• undersøker

A good tip is:

1. Make an e- or uh-like sound in the front of the mouth.
2. Round your lips more than you would in English.

It takes practice, but that is the general idea.