Final answer:
Alexander Kerensky led the Provisional Government, fragmented in its influence due to challenges by the soviets. Had the government agreed to peace and focused on domestic issues, it could have potentially weakened the Bolsheviks' appeal, but overarching issues may have still offered them support.
Step-by-step explanation:
The Provisional Central Power, also known as the Provisional Government, was led by Alexander Kerensky. This government held a precarious position as it was challenged by the Petrograd Soviet and other soviets, which held significant sway over workers, soldiers, and peasants, and demanded "peace, land, and bread." The Provisional Government was responsible for legal reforms but failed to address the immediate needs of the Russian people or to withdraw the Russian army from the front lines of World War I. This inability to meet the urgent demands of the constituency undermined its influence, thereby fueling support for the Bolsheviks, who capitalized on the public's grievances.
If the Provisional Government had agreed to a peace with the Central Powers and prioritized Russia's internal issues, the historical trajectory might have been starkly different. Such an agreement could have relieved the pressures of the war and potentially placated the populace's desire for peace, possibly reducing support for the Bolsheviks. However, the deep-rooted socioeconomic issues might have still provided fertile ground for the Bolsheviks' promises of radical change, making it uncertain how much influence the provisional government could have maintained even with a peace agreement.