Question

Let P7(x) be the real vector space of polynomials in x with degree at most 7, together with the zero polynomial. For r = 1, 2, … , 7, define
sr(x) = x(x - 1) ⋯ (x − (r - 1)) and s0(x) = 1.
Consider the fact that B = {s0(x), s1(x), … , s7(x)} is a basis of P7(𝑥).
If
$x^5=\sum\limits_{k=0}^7a_{5,k}s_k(x),$
where a5,k ∈ $\R$, then a5,2 equals ___________ (rounded off to two decimal places)

Answer 1

The correct answer is 14.95 to 15.05. (approx)