How can we reconcile God's choosing of Adam and Noah in Surah Al-Imran with Adam and Eve making partners with God after they were blessed with a righteous child, as stated in Surah Al-A'raf, where they named their son "Abd"?

The scholars differed in the interpretation of the Almighty's saying: "But when He gave them a goodly child, they ascribed to Him partners in what He had given them." The most accurate view is that it refers to the polytheistic descendants of Adam and Eve, and not Adam and Eve themselves. This is supported by the Almighty's saying: "Exalted be Allah above what they associate with Him!" Had it been intended for Adam and Eve, it would have said "they both associate." This view is relied upon by the verified exegetes. As for the view that the verse refers to Adam and Eve, weak hadiths and narrations have been reported concerning it.

The prophets are infallible from major sins and polytheism.