Een factor is belangrijk.

Een is the indefinite article, like a/an in English. You use it when you mean a factor in a general or non-specific way.

The noun factor is a de-word, so the definite form is de factor. Het factor is not correct in standard Dutch.

One useful thing to remember: een is used with both de-words and het-words, so you have to learn the definite article separately.

Because factor is singular.

Dutch verb forms agree with the subject:

• een factor is
• factoren zijn

So if the subject becomes plural, the verb changes too.

Because belangrijk comes after is and works as a predicate adjective. In Dutch, predicate adjectives normally stay in the basic form.

So you say:

• De factor is belangrijk.
• De factoren zijn belangrijk.

But when the adjective comes directly before a noun, it usually takes -e:

• een belangrijke factor
• de belangrijke factor

In this sentence, yes: it is basically subject + verb + adjective.

• Een factor = subject
• is = verb
• belangrijk = adjective

But the broader Dutch rule is that the finite verb usually comes second in a main clause. This sentence follows that rule naturally.

Yes, but that is a different structure.

• een belangrijke factor is a noun phrase
• Een factor is belangrijk. is a full sentence

In een belangrijke factor, the adjective comes before the noun and directly describes it.

In Een factor is belangrijk, the adjective comes after is and describes the subject through the verb.

The plural is factoren.

So:

• singular: een factor
• plural: factoren

And the sentence becomes:

• Factoren zijn belangrijk.

Notice that both the noun and the verb change.

Usually not.

• een as the article is normally unstressed and pronounced very weakly, roughly like uhn
• één means one and is stressed

So in Een factor is belangrijk, the first word is the unstressed article een, not the number één.

No. Unlike German, Dutch does not capitalize all nouns.

So factor stays lowercase unless it starts the sentence or is part of a proper name.

In Een factor is belangrijk, only Een is capitalized because it is the first word of the sentence.