应该改为 The teacher together with some students 【is】 visiting the factory.
本句的主语是The teacher,单数.如果把together with 换成 and ,主语就是复数概念了.
注意：当主语是用with,together with,as well as,like,besides,except,but等连接的两个词时,谓语动词与第一个词一致,即“就前一致”.如 Tom with his classmates is playing outside./ Mr.John as well as his students is talking in the office.