Nie mam kleju, więc córka nie może dokończyć zadania.

Because Polish often uses the genitive after a negated verb.

• mam klej = I have glue
• nie mam kleju = I don’t have glue

The base noun is klej. Its genitive singular form is kleju.

This is a very common pattern in Polish:

• Mam czas. = I have time.
• Nie mam czasu. = I don’t have time.

So in this sentence, kleju is there because mam is negated by nie.

For the same general reason: negation often changes the object to the genitive.

The positive version would normally be:

• Córka może dokończyć zadanie. = The daughter can finish the task.

But with negation:

• Córka nie może dokończyć zadania. = The daughter cannot finish the task.

Here:

• zadanie = nominative/accusative singular
• zadania = genitive singular

So zadania appears because the phrase nie może dokończyć is negative.

Because in Polish, nie is written separately from verbs.

So:

• nie mam = I do not have
• nie może = he/she cannot / is not able to

This is a basic spelling rule in Polish:

• with verbs, nie is usually separate
• with many adjectives and some other words, it is often written together

Examples:

• nie wiem = I don’t know
• nie robi = he/she doesn’t do

Because córka is the subject of the second clause, and subjects are usually in the nominative case.

In córka nie może dokończyć zadania:

• córka = the person doing or not doing the action
• so it stays nominative: córka

Compare:

• Córka czyta. = The daughter is reading.
• Widzę córkę. = I see the daughter.

In the second sentence, córkę is the object, so the case changes.

Because Polish often expresses can / be able to with the verb móc plus an infinitive.

Here:

• może = can / is able to
• dokończyć = to finish / to complete

So:

• nie może dokończyć literally means cannot finish

This works like:

• Mogę iść. = I can go.
• Nie mogą zostać. = They cannot stay.

Dokończyć means to finish something that has already been started.

Very roughly:

• kończyć = to be finishing / to finish (imperfective)
• skończyć = to finish / complete (perfective)
• dokończyć = to finish off / finish what was left incomplete (perfective)

In this sentence, dokończyć zadania suggests the daughter has already started the task, but cannot bring it to completion.

So dokończyć is a very natural choice if the idea is finish the rest of it.

Because więc joins two clauses, and in Polish that normally requires a comma.

Here the sentence has two parts:

1. Nie mam kleju
2. więc córka nie może dokończyć zadania

So the comma is standard Polish punctuation.

This is similar to English punctuation with linking words like so, though Polish is often stricter about using the comma.

Yes, here więc means so, therefore, or thus.

It connects cause and result:

• Nie mam kleju = cause
• więc córka nie może dokończyć zadania = result

Depending on context, więc can sound a little more clearly logical than casual English so, but in many everyday sentences so is a perfectly good translation.

Yes. The verb mieć = to have is common and somewhat irregular.

Some present-tense forms are:

• mam = I have
• masz = you have
• ma = he/she/it has
• mamy = we have
• macie = you all have
• mają = they have

So mam is simply the 1st person singular form: I have.

Yes. Polish word order is more flexible than English, because case endings show grammatical roles.

The given sentence is a natural, neutral version:

• Nie mam kleju, więc córka nie może dokończyć zadania.

Other word orders are possible, but they change the emphasis. For example:

• Córka nie może więc dokończyć zadania.
• Więc córka nie może dokończyć zadania.

These are not necessarily wrong, but the original version is the most straightforward for ordinary use.

Because Polish often leaves out possessive words like my, your, his, etc. when the meaning is already clear from context.

So:

• córka can mean the daughter or my daughter, depending on context

If the speaker’s daughter is already understood, córka alone sounds natural.

If you want to make it explicit, you can say:

• Nie mam kleju, więc moja córka nie może dokończyć zadania.

That is also correct, just a bit more explicit.

A few useful notes:

• nie sounds roughly like nyeh
• mam sounds close to mahm
• kleju is roughly KLEH-yoo
• więc is roughly vyents
• córka is roughly TSOOR-ka
• może is roughly MO-zhe
• dokończyć is roughly do-KON-chich
• zadania is roughly za-DA-nya

A few letters to notice:

• ó sounds like u
• cz sounds like English ch
• rz/ż sounds like the s in measure
• ń sounds like ny
• ę often changes slightly depending on the sound after it

The spelling may look difficult at first, but the pronunciation becomes much easier once you learn the common letter combinations.