In theological terms, a debate exists over the peccability or impeccability of Christ. Peccability means that a person is capable of sin. Conversely, impeccability is that one is incapable of sin. So, if one believes in the impeccability of Jesus, they believe that He could not have sinned. If one believes in the peccability of Christ, they believe that He had a choice in the matter and that He simply chose not to sin, but that He could have given in to temptation.
Could Jesus have sinned? Was He truly tempted? Did He have the choice to give in to temptation?