Time-resolved spectroscopy is performed on eight bright, long gamma-ray bursts (GRBs) dominated by single emission pulses that were observed with the {it Fermi Gamma-ray Space Telescope}. Fitting the prompt radiation of GRBs by empirical spectral forms such as the Band function leads to ambiguous conclusions about the physical model for the prompt radiation. Moreover, the Band function is often inadequate to fit the data. The GRB spectrum is therefore modeled with two emission components consisting of optically thin nonthermal synchrotron radiation from relativistic electrons and, when significant, thermal emission from a jet photosphere, which is represented by a blackbody spectrum. To produce an acceptable fit, the addition of a blackbody component is required in 5 out of the 8 cases. We also find that the low-energy spectral index alpha is consistent with a synchrotron component with alpha = -0.81pm 0.1. This value lies between the limiting values of alpha = -2/3 and alpha = -3/2 for electrons in the slow and fast-cooling regimes, respectively, suggesting ongoing acceleration at the emission site. The blackbody component can be more significant when using a physical synchrotron model instead of the Band function, illustrating that the Band function does not serve as a good proxy for a nonthermal synchrotron emission component. The temperature and characteristic emission-region size of the blackbody component are found to, respectively, decrease and increase as power laws with time during the prompt phase. In addition, we find that the blackbody and nonthermal components have separate temporal behaviors.
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