A novel polynomial guidance law is proposed for flight vehicle terminal guidance, subject to multiple constraints including launch angle, impact angle, impact time, and zero terminal acceleration. This approach reconstructs the flight path angle profile into two components. One component satisfies the constraints. The other ensures target interception. The constraint-oriented component is formulated as a polynomial function of the relative range-to-go. Based on this reconstruction framework, a new linearization approach is introduced to handle the nonlinear engagement kinematics. A closed-form guidance law is then derived to satisfy multiple constraints, and its convergence is analyzed theoretically. To optimize the control effort, a data-driven method is subsequently incorporated into the framework. Numerical simulation results show that the proposed guidance law achieves multiple constraints with high precision. Compared with existing methods, it also requires less control effort. Specifically, the impact angle error is within 0.02°, and the impact time error is within 0.05 s.