Polynomial Function Help

LMI

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Hello. I tried solving this question but I think my answer is wrong. I would like some help, thank you.
 

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You can't assume the 6th difference will be constant if there is only one value. Check your arithmetic, especially from the third differences, you have some errors there.
 
I did the math again but this time I got -4. What should I write for the degree and leading coefficient? I don't understand how do it... Should I say the degree is one because I can't assume the 6th difference will be constant if there is only one value?
 

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