Alternate Expression (Interpolation with Polynomials)

[dmanniteaux]

Difficulty : College

Homework Statement

The Attempt at a Solution

I am unsure how to approach this question. I think it involves a process where you add an expression & and subtract it (or multiply & divide) in order to manipulate the equation and rearrange it or reorder it. I've already tried expanding the (x-c)^i part, but later realized x^i - c^i does not equal (x-c)^i.

Any help would be much appreciated

Thanks!

 

[Joffan]

You might need to use an induction proof - so that you can just focus on the highest-order term.

 

[Dick]

Use the binomial theorem to expand (x-c)^i.