Resource constraint sensors of a Wireless Sensor Network (WSN) cannot afford the use of costly encryption techniques like public key while dealing with sensitive data. So symmetric key encryption techniques are preferred where it is essential to have the same cryptographic key between communicating parties. To this end, keys are preloaded into the nodes before deployment and are to be established once they get deployed in the target area. This entire process is called key predistribution. In this paper we propose one such scheme using unique factorization of polynomials over Finite Fields. To the best of our knowledge such an elegant use of Algebra is being done for the first time in WSN literature. The best part of the scheme is large number of node support with very small and uniform key ring per node. However the resiliency is not good. For this reason we use a special technique based on Reed Muller codes proposed recently by Sarkar, Saha and Chowdhury in 2010. The combined scheme has good resiliency with huge node support using very less keys per node.