As a married man, is it permissible for my wife to work with me in a factory, or is it forbidden?

If you mean your wife, there is no harm in her working if she adheres to the Islamic hijab. However, if you mean a woman who is not your wife, it is not permissible to work in a factory where men and women intermingle without adhering to Islamic regulations such as the hijab, not speaking seductively, avoiding physical contact, and refraining from unlawful seclusion, which is when a man and a woman meet in a place where they are safe from the entry of a third party.