There is an extra syllable, and you're correct – it's -un.

Copying my answer from a similar question on a different sentence:

Yes, it's the nominative indefinite ending. In formal MSA (and Qurani Arabic), you have three cases and six endings:

Nominative: -u (definite) / -un (indefinite)
Accusative: -a (definite) / -an (indefinite)
Genitive: -i (definite) / -in (indefinite)

The nominative is used as you'd expect – for the subject of the sentence.

تَكَلَّمَ رَجُلٌ لَطيفٌ مَعِي أَمسِ
takallama rajulun latifun ma3i amsi
"A nice man spoke to me yesterday"

يُعجِبنا البَيتُ الجَديدُ
yu3jibna l-baytu l-jadidu
"We like the new house" ("The new house pleases us")

The accusative is also used as you'd expect – for the direct object of the verb. Note that a final alif will always be added for the accusative indefinite ending (except after a ta' marbuta).

هَل اِشتَرَيتَ هاتِفاً غاليّاً؟
hal ištarayta hatifan ghaliyan?
"Did you buy an expensive phone?"

أُحِبّ القِراءَةَ
u7ibb al-qira'ata
"I love reading"

The genitive is used both on the possessor in an idafah construct (idafah being the genitive construct in Arabic), and on nouns following prepositions.

عاصِمةِ مِصر
3aSimati miSr
"The capital of Egypt"

(Note that the definite genitive ending is used, not the indefinite, even though there is no definite article on the noun. This is due to idafah, but I won't go into detail on that here)

رَأَيتُهُ في كِتابٍ قَديمٍ
ra'aytuhu fi kitabin qadimin
"I saw it in an old book"

المَفاتِحُ عَلى الطاوِلةِ
al-mafati7u 3ala T-Tawilati
"The keys are on the table"

Note that in more casual MSA, the endings aren't used as much. For example, the last sentence, "المفاتح على الطاولة", would be more commonly pronounced "al-mafati7 3ala T-Tawila". Also in casual MSA, at the end of the sentence, the ending isn't used; this can be seen in the Duolingo exercise; "baytun kabir", not "baytun kabirun" (which would be the official formal pronunciation). Furthermore, the cases disappear completely in the dialects.