This question sounds much like homework to me, thus I will only give you hints at what to look for:

1. Define what polynomial division is.
2. Every Polynom can be written in two standard forms (at least if you also allow imaginary numbers, which won't be necessary for our case). Identify those two forms.
3. Are those two forms of a given polynomial unique? Why? Why not?
4. You are looking for a f(X) which satisfies f(X_i) = Y_i for all i between 1 and the length of your data column.
5. Start with the easy cases of i=0, i=1 and i=2.
6. Can you extend a solution for i=1 to i=2?
7. Can you extend a solution for i=n to i=n+1?

perl -MHTTP::Daemon -MHTTP::Response -MLWP::Simple -e ' ;    # The  
$d = new HTTP::Daemon and fork and getprint $d->url and exit;#spider
($c = $d->accept())->get_request(); $c->send_response( new   #in the
HTTP::Response(200,$_,$_,qq(Just another Perl hacker\n))); ' #  web
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