Polis suçu araştırıyor.

Because suçu is the definite direct object form of suç.

The base noun is suç = crime.
When a noun is a specific object in Turkish, it often takes the accusative ending. Here, that ending is -u.

So:

• suç = crime
• suçu = the crime / the specific crime

There is also a sound change:

• suç + u becomes suçu

The final ç stays, and Turkish connects the ending directly here.

It marks the noun as a specific, definite object.

In English, this often corresponds to the or sometimes just a specific object understood from context.

Compare:

• Polis suç araştırıyor would sound unnatural here
• Polis suçu araştırıyor = The police is/are investigating the crime

So -u tells you the action is directed at a particular crime, not crime in general.

Because araştırıyor is the present continuous form, used for an action happening right now or around the present time.

It comes from:

• araştırmak = to investigate / to research
• stem: araştır-
• present continuous ending: -ıyor

So:

• araştırıyor = is investigating / are investigating

By contrast:

• araştırır is more like investigates, does investigate, or usually investigates, depending on context.

In this sentence, araştırıyor is the natural choice for an ongoing action.

Because of vowel harmony.

The present continuous suffix has four forms:

• -ıyor
• -iyor
• -uyor
• -üyor

The form depends on the last vowel before the suffix. In araştır-, the relevant vowel leads to -ıyor.

So:

• araştırıyor is the correct harmonized form.

This is a very common Turkish pattern, and you will see it with many suffixes.

Because Turkish does not need a separate auxiliary verb like English does here.

In English, you say:

• is investigating
• are investigating

In Turkish, that meaning is built into the verb itself:

• araştırıyor

So one word already contains the idea of is investigating / are investigating.

Because polis can be used as a collective or generic noun in Turkish.

Depending on context, polis can mean:

• a police officer
• the police as an institution or body

So Polis suçu araştırıyor can naturally mean The police are investigating the crime.

If you say polisler, that clearly means police officers in the plural:

• Polisler suçu araştırıyor = The police officers are investigating the crime

Both are possible, but polis is very natural here.

Because Turkish and English handle this idea differently.

In English, police is usually treated as plural:

• The police are investigating the crime

In Turkish, polis here is often treated as a singular collective noun, so the verb appears in third person singular:

• Polis suçu araştırıyor

That is completely normal Turkish.

The basic word order is:

Subject + Object + Verb

So:

• Polis = subject
• suçu = object
• araştırıyor = verb

This is the most neutral Turkish order:

• Polis suçu araştırıyor.

Turkish often puts the verb at the end.

Yes. Turkish word order is flexible, but changing it changes focus or emphasis.

For example:

• Polis suçu araştırıyor. = neutral
• Suçu polis araştırıyor. = It is the police who are investigating the crime
• Araştırıyor polis suçu. = possible in special contexts, but less neutral

So the original sentence is the most straightforward and standard version.

Not always. Araştırmak can mean:

• to investigate
• to research
• to look into

The exact meaning depends on context.

With suç = crime, the natural meaning is:

• to investigate the crime

So in this sentence, investigate is the best translation.

Turkish has no separate word exactly like English the.

Instead, definiteness is often shown in other ways, especially with the accusative ending on direct objects.

So in this sentence, suçu helps give the sense of the crime or that specific crime.

That is why Turkish can express the meaning without a separate article.

A rough guide is:

• Polis ≈ po-LIS
• suçu ≈ soo-joo or soo-chu depending on how carefully you are aiming for the Turkish sounds
• araştırıyor ≈ a-ra-sh-tuh-RI-yor

A few important pronunciation notes:

• ş sounds like sh
• ç sounds like ch
• ı is a Turkish vowel with no exact English equivalent; it is not the same as i

So araştırıyor contains both ş and ı, which can take some practice.

The dictionary form is araştırmak.

In Turkish, verbs are usually listed in dictionaries with -mak or -mek:

• araştırmak = to investigate / to research

To make the sentence form, Turkish removes -mak and adds tense/person endings:

• araştırmak
• stem: araştır-
• araştırıyor = is investigating / are investigating

Yes, in some contexts polis can refer to a police officer.

So depending on the situation, Polis suçu araştırıyor could mean:

• The police are investigating the crime
• A police officer is investigating the crime
• The police officer is investigating the crime

Usually, context tells you which one is intended. Without context, the sentence can be a little broad in English.