Poculum ex argento factum est.

Poculum is nominative singular neuter.

It is the subject of the sentence: the thing that was made.
The dictionary form is also poculum, meaning cup or goblet.

Because it is neuter singular, any adjective or participle agreeing with it must also be neuter singular, which is why we get factum.

Because ex is a preposition meaning out of / from, and it takes the ablative case.

So:

• argentum = silver, in the nominative/accusative form
• argento = silver, in the ablative singular

In this sentence, ex argento means out of silver or more naturally from silver / made of silver.

It is ablative because the preposition ex requires the ablative.

This is a very common Latin pattern:

• ex urbe = out of the city
• ex aqua = out of water
• ex argento = out of silver

So the case is not chosen randomly; it is required by the preposition.

Factum est is the perfect passive of facio.

It is built from:

• factum = the perfect passive participle
• est = is, from sum

Together they mean was made.

This is a standard Latin way of forming the perfect passive:

• factus est = he was made / he was done
• facta est = she/it was made
• factum est = it was made

So although est by itself usually means is, here the whole expression factum est means was made.

Because factum has to agree with poculum.

Poculum is:

• singular
• neuter
• nominative

So the participle must also be:

• singular
• neuter
• nominative

That gives factum.

Compare:

• servus factus est = the slave was made
• puella facta est = the girl was made
• poculum factum est = the cup was made

Because in Latin the perfect passive uses:

• a perfect passive participle
• plus a present form of sum

So:

• factum est literally looks like made is
• but idiomatically it means was made or has been made

This is just how Latin expresses that tense in the passive voice.

Yes. Latin word order is much freer than English word order because the endings show the grammar.

So all of these could mean the same thing:

• Poculum ex argento factum est.
• Ex argento poculum factum est.
• Factum est poculum ex argento.

However, the original order is natural and clear.
Often Latin places important information, such as factum est, near the end.

More literally, ex argento means out of silver or from silver.

In normal English, we usually say made of silver, so that is the smoothest translation. But the Latin wording really does involve the idea of material or source: the cup was made from silver.

Classical Latin has no articles like English a, an, or the.

So poculum can mean:

• a cup
• the cup
• just cup

The context decides which is best in English.

That is why one Latin sentence can often be translated in more than one natural way.

The dictionary forms are:

• poculum, poculi — cup, goblet
• ex — out of, from
• argentum, argenti — silver
• facio, facere, feci, factum — make, do

In the sentence:

• poculum is nominative singular
• argento is ablative singular after ex
• factum est is the perfect passive form built from facio

Yes. Facio is a very common verb that can mean do or make, depending on context.

Its principal parts are:

• facio
• facere
• feci
• factum

From that last principal part, factum, Latin builds passive forms such as factum est.

So in this sentence, factum est means was made.

Yes, but ex + ablative is a very standard and clear way to express material, especially when something is made from something.

So ex argento factum is a normal way to say made of silver.

You may also meet other constructions in Latin for material in different contexts, but for a beginner this sentence is a very good model to remember:

• ex
  • ablative = out of / from / made of