Við förgum spilliefninu.

Because farga is the infinitive form, meaning the dictionary form to dispose of / to get rid of.

In the sentence, the verb has to be conjugated to match við (we), so Icelandic uses the 1st person plural present form:

• að farga = to dispose of
• við förgum = we dispose of

So förgum means we dispose of / we are disposing of.

This is بسبب an Icelandic sound change usually called u-umlaut.

The verb stem is farg-, but when the ending -um is added, the a in the stem changes to ö:

• underlying pattern: farg + um
• actual form: förgum

This kind of vowel change is very common in Icelandic and is something you simply learn as part of the conjugation pattern.

Here -um is the ending for the 1st person plural present tense of the verb.

So in this sentence:

• við = we
• förg-um = dispose-we

You do not translate -um by itself in English, but it is the part that tells you the subject is we.

Because it is:

• singular
• definite = the hazardous waste / the pollutant
• in the dative case

The base noun is spilliefni. Icelandic usually adds the definite article onto the end of the noun instead of using a separate word like English the.

So:

• spilliefni = hazardous waste / a hazardous substance
• spilliefnið = the hazardous waste (nominative/accusative)
• spilliefninu = the hazardous waste (dative)

In this sentence, the verb requires the dative, so you get spilliefninu.

Because the verb að farga takes a dative object.

This is something you have to learn with the verb. In Icelandic, many verbs do not take the accusative object that an English speaker might expect.

So the dictionary information is effectively:

• að farga e-u = to dispose of something
  (e-u is a shorthand showing the noun/pronoun should be in the dative)

That is why the sentence uses spilliefninu rather than a nominative or accusative-looking form.

Yes, in terms of meaning, it is the thing being disposed of, so an English speaker will often think of it as the object of the verb.

But in Icelandic, objects are not always accusative. Some verbs govern:

• accusative
• dative
• genitive

So here the object is in the dative because farga requires that case.

Because Icelandic usually uses a suffixed definite article.

Instead of putting a separate word before the noun, Icelandic often attaches the article to the end:

• spilliefni = hazardous waste
• spilliefnið / spilliefninu = the hazardous waste, in different cases

So the the is built into spilliefninu.

In normal modern Icelandic, við is usually needed.

Even though the verb ending -um already shows we, Icelandic generally does not drop subject pronouns the way Spanish or Italian often can.

So the normal full sentence is:

• Við förgum spilliefninu.

Without við, the sentence would usually sound incomplete unless it appeared in a special context, such as instructions, slogans, or very marked style.

You should learn it as:

• að farga e-u

That tells you two important things at once:

1. the infinitive is að farga
2. the verb takes a dative object

That second part is very important, because if you only memorize að farga without the case pattern, you may produce the wrong noun form later.

Yes. Without the suffixed article, spilliefni is indefinite.

So the contrast is roughly:

• Við förgum spilliefni = We dispose of hazardous waste / hazardous substances
• Við förgum spilliefninu = We dispose of the hazardous waste

The version with -nu refers to a more specific, identifiable thing.

Here it is singular definite dative: spilliefninu.

Even though English may sometimes use a plural expression like hazardous materials, Icelandic can use a singular noun for a mass or category of material.

So in this sentence, you should treat spilliefninu as a singular noun form.

Yes, but the given order is the most neutral one.

• Við förgum spilliefninu. = neutral statement

You can move things for emphasis, but Icelandic main clauses usually keep the finite verb in second position:

• Spilliefninu förgum við. = marked/emphatic, something like The hazardous waste, we dispose of
• Nú förgum við spilliefninu. = Now we dispose of the hazardous waste

So the original sentence is the normal basic order for a plain statement.