First of all, Zhao Gao won the trust of Qin Shihuang and had great power. Qin Shihuang was the first monarch to use the title of "Emperor" in the history of China. After Qin Shihuang unified the world, he inherited the county system, centralization, unified measurement and laws and regulations of Shang Yang's political reform, which laid an autocratic political pattern in the political history of China for more than 2,000 years. Li Zhi, a thinker in the Ming Dynasty, praised him as "an emperor through the ages". On the other hand, Qin Shihuang also carried out many large-scale projects during his reign, including the construction of the Great Wall, Epang Palace and Mount Li. Impatient administration made the people overworked, which was an important reason for the rapid decline of the Qin Dynasty three years after his death. Zhao Gao was always by Qin Shihuang's side, so Qin Shihuang learned many ways to manage a political country. At the same time, he also knows what the weakness of the court is, which ministers are loyal and which are treacherous. It was because Qin Shihuang trusted him and was unprepared that he was able to hide the testamentary edict after Qin Shihuang's death, and then encouraged Qin Ershi and Hu Hai to inherit the throne. Because Hu Hai was weak, Zhao Gao could completely control him, so he just set up a puppet.
Secondly, Qin Ershi and Hu Hai indulge in debauchery and don't ask about state affairs. Most of the affairs of governing the country are left to Zhao Gao. So Zhao Gao knew all his weaknesses and strengths, and he prescribed the right medicine. Getting rid of Hu Hai is a piece of cake.
So Zhao Gao killed Hu Hai, not only because Zhao Gao sought power and usurped the throne, but also because Hu Hai himself was too backward. Willing to be a puppet.