Let d(n) represent the number of diagonals of a polygon of n sides. Here is a table of values of d(n).

Question

n 3 4 5 6 7 8 9 10 11
d(n)0 2 5 9 14 20 27 35 44

Find a polynomial formula for d(n) in terms of n

Answer 1

check the differences:
1st: 2 3 4 5 6 ...
2nd: 1 1 1 1 1

So, it will be a quadratic

d = an^2+bn+c

Plug in three points to find a,b,c