This study examines factors influencing teachers' intention to adopt Generative AI technologies in education by extending the Technology Acceptance Model (TAM). The proposed comprehensive model incorporates both external factors (exposure to AI information, information credibility, and institutional support) and internal factors (intrinsic motivation and self-efficacy). A survey of 400 teachers reveals that teachers' exposure to credible AI information positively influences perceptions of Generative AI usefulness, which ultimately impacts their intention to use AI. Importantly, institutional support has both direct and indirect effects on teachers' intention to use AI, with the indirect effect mediated by the internal factors of intrinsic motivation and self-efficacy. This research complements TAM theory by integrating psychological and contextual factors, offering a nuanced framework for understanding Generative AI adoption in educational settings. The findings suggest that for educational leaders and policymakers, developing strategies that allocate resources for infrastructure, technical support, and professional development--such as Generative AI training programs--will be crucial in driving Generative AI adoption among teachers. By addressing both external and internal determinants, this study provides a comprehensive perspective of the dynamics behind technology acceptance in the classroom.