This paper deals with the linear quadratic regulation problems for the linear discrete-time systems with $l$ input delays. The design of the optimal control law is transformed into solving one Diophantine equation and one spectral factorization with delays. A new and simple approach for the spectral factorization is proposed based on reorganized innovation analysis. The calculation of spectral factor comes down to solving ${l}+1$ Riccati equations with the same dimension as the original systems.