In this excerpt form act i scene i of shakespeare’s richard iii what two purposes does richard soliloquy appear to serve?

The first purpose that Richard's soliloquy appears to serve is to reveal the motivations and personality of the character - we can see that he hates himself because he was basically a hunchback, so he was pretty self-conscious about it. He also reveals in the first scene what he intends to do throughout the play. 

As for the second purpose, I'd choose the answer - it informs the audience about the background of the plot, as it gives us reasons why Richard decided to do what he did. 

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c. barbarians with unexpected intelligence