Show that for any number $c$, a polynomial $P(x) = a_0 + a_1 x^1 + a_2 x^2 + \cdots a_n x^n$ can be written in the form $P(x) = b_0 + b_1(x - c) + b_2(x - c)^2 + b_3(x - c)^3 \cdots b_n(x - c)^n$ if $b_0 = P(c)$

Question

anonymous · Answer

So we get to chose the values for b?

parthkohli · Answer

Proved it on the other site.

anonymous · Answer

Also what is with the $ b_n (x-n)^n $?  Why not $ b_n (x-c)^n $?

parthkohli · Answer

Sorry, edited. No need for help now; closing!

parthkohli · Answer

It's like I am standing in two queues, and I reach the counter first on the other queue :)

unklerhaukus · Answer

whats the answer parth?

parthkohli · Answer

http://math.stackexchange.com/questions/265311/polynomial-rewriting-proof/265314#265314

shubhamsrg · Answer

i see..that was cool.. B|

unklerhaukus · Answer

i dont get it

parthkohli · Answer

What? It's pretty simple.$$P(x) = a_0((x - c) + c)^1 + a_1((x - c)  + c)^2 \cdots$$A special case of the binomial theorem.

unklerhaukus · Answer

do you mean to start at ^0 ?