Investigaron el crimen.

Investigaron is the third-person plural preterite form of investigar (to investigate).

So it can mean:

• they investigated
• in some contexts, you all investigated (for ustedes)

In Spain, ustedes is usually formal, so without more context, many learners would first read it as they investigated.

Spanish often leaves out subject pronouns because the verb ending already shows who the subject is.

• investigaron already tells you it is third-person plural
• so Spanish does not need ellos or ellas

You could say:

• Ellos investigaron el crimen

but it is usually unnecessary unless you want emphasis, contrast, or clarity.

Spanish often uses the definite article more than English does.

El crimen means the crime, so it usually refers to a specific crime that is already known from the context.

• Investigaron el crimen = They investigated the crime

If you said investigaron un crimen, that would mean they investigated a crime, usually introducing it as new information.

The preterite is used for a completed action in the past.

So investigaron el crimen presents the investigation as a finished event:

• They investigated the crime

If you wanted to describe an ongoing or repeated past action, Spanish would often use the imperfect instead:

• Investigaban el crimen = They were investigating the crime / They used to investigate the crime

So the preterite here gives a sense of a completed action.

The infinitive is investigar (to investigate).

It is a regular -ar verb. In the preterite, the forms are:

• yo investigué
• tú investigaste
• él/ella/usted investigó
• nosotros/nosotras investigamos
• vosotros/vosotras investigasteis
• ellos/ellas/ustedes investigaron

Notice the spelling in investigué: the u is added to keep the hard g sound before é.

Yes, grammatically it can, because investigaron is also the ustedes form.

However, in Spain, ustedes is mainly used in formal situations. In everyday informal speech in most of Spain, you all investigated would usually be:

• investigasteis (for vosotros/vosotras)

So in a Spain-focused course, investigaron will more often be understood as they investigated, unless the context clearly shows formal ustedes.

A simple pronunciation guide:

• investigaron → in-ves-tee-ga-RON
• el → el
• crimen → CRI-men

Stress:

• investigaron is stressed on -ga-
• crimen is stressed on cri-

A rough English-style approximation might be:

• een-ves-tee-ga-RON el KREE-men

The r in crimen is a tapped Spanish r, not an English r.

Because its grammatical gender is masculine: el crimen.

Spanish noun gender is not always predictable just from meaning. While many nouns ending in -a are feminine and many ending in -o are masculine, words ending in other letters have to be learned individually.

So you simply learn it as:

• el crimen

Yes, Spanish word order is more flexible than English word order, although Investigaron el crimen is a very normal neutral order.

This sentence is basically:

• verb + object

Other word orders are possible for emphasis, for example:

• El crimen lo investigaron ellos
• Ellos investigaron el crimen

But the original version sounds natural and straightforward.

No. Investigar means to investigate, not to solve.

So:

• Investigaron el crimen = They investigated the crime

If you want they solved the crime, Spanish would use something like:

• Resol vieron el crimen
  or more naturally in many contexts:
• Resolvieron el caso

Investigating and solving are related ideas, but they are not the same.

Not normally.

Investigaron el crimen means a completed past action: They investigated the crime.

To say They were investigating the crime, Spanish would usually say:

• Investigaban el crimen
• Estaban investigando el crimen

So if you see investigaron, think of a finished action, not an ongoing one.