Why is ‘prejudice’ syllabified as Prej-u-dice?

Prejudice is syllabified as /ˈprɛd͡ʒ.ə.dəs/ and not */ˈprɛ.d͡ʒə.dəs/ because the lax vowel /ɛ/ doesn't occur at the end of syllables in English and therefore it should have a coda—a consonant after it (see Maximal Onset Principle).

Also according to John Wells' syllabification, ‘consonants are syllabified with the more strongly stressed of two flanking syllables’. The first syllable in prejudice has primary stress on it, so the /d͡ʒ/ is syllabified with that syllable, giving /ˈprɛd͡ʒ.ə.dəs/.

Merriam-Webster and American Heritage Dictionary give:

prej·​u·​dice
prej·u·diced, prej·u·dic·ing, prej·u·dic·es

So yes, it should be hyphenated prej·​u·​dice.