Large language models (LLMs) have recently been adopted for recommendation by framing user preference modeling as a language generation problem. However, existing latent reasoning approaches typically represent user intent with a single latent vector, which struggles to capture the inherently multi-faceted nature of user preferences. We propose Factorized Latent Reasoning (FLR), a novel framework for LLM-based sequential recommendation that decomposes latent reasoning into multiple disentangled preference factors. FLR introduces a lightweight multi-factor attention module that iteratively refines a latent thought representation, where each factor attends to distinct aspects of the user's interaction history. To encourage diversity and specialization, we design orthogonality, attention diversity, and sparsity regularization objectives, and dynamically aggregate factor contributions for the final prediction. We further integrate FLR with an efficient reinforcement learning strategy based on group-relative policy optimization, enabling stable alignment directly in the latent reasoning space. Experiments on multiple benchmarks show that FLR consistently outperforms strong baselines while improving robustness and interpretability.