Question

Where are protein synthesized inside the cell

Answer 1

Protein synthesis is one of the most important biological processes by which individual cells build specific proteins in order to function.
Protein synthesis occurs in the rough endoplasmic reticulum, ribosomes and in the nucleus. Note that Rough ER contains ribosomes.

The DNA of the cell is read in certain sections that contain the code for a specific protein. In eukaryotic cells, transcription (process of changing DNA to RNA) process occurs in the nucleus. Afterwards, translation (mRNA to specific amino acids) occurs with the help of the ribosomes in the cytoplasm. In prokaryotes, because there is no nucleus to separate the processes of transcription and translation, when bacterial genes are transcribed, their transcripts can immediately be translated.
Because rough ER is studded with ribosomes, translation also occurs in the rough ER.