Phenotyping electronic health records (EHR)focuses on defining meaningful patient groups (e.g., heart failure group and diabetes group) and identifying the temporal evolution of patients in those groups. Tensor factorization has been an effective tool for phenotyping. Most of the existing works assume either a static patient representation with aggregate data or only model temporal data. However, real EHR data contain both temporal (e.g., longitudinal clinical visits) and static information (e.g., patient demographics), which are difficult to model simultaneously. In this paper, we propose Temporal And Static TEnsor factorization (TASTE) that jointly models both static and temporal information to extract phenotypes.TASTE combines the PARAFAC2 model with non-negative matrix factorization to model a temporal and a static tensor. To fit the proposed model, we transform the original problem into simpler ones which are optimally solved in an alternating fashion. For each of the sub-problems, our proposed mathematical re-formulations lead to efficient sub-problem solvers. Comprehensive experiments on large EHR data from a heart failure (HF) study confirmed that TASTE is up to 14× faster than several baselines and the resulting phenotypes were confirmed to be clinically meaningful by a cardiologist. Using 60 phenotypes extracted by TASTE, a simple logistic regression can achieve the same level of area under the curve (AUC) for HF prediction compared to a deep learning model using recurrent neural networks (RNN) with 345 features.