There's this problem in my algebra book:
Problem 101. Imagine that the polynomial is converted to the standard form (the sum of powers of x with numerical coefficients). What is the sum of all the coefficients?
My solution. The solution of this problem is I think, am I right?
In this particular problem, it is not necessary to use binomial coefficients. Do you see that the sum of coefficients of a polynomial P is P(1)?
On the other hand, P(1) gives you the sum of coefficients.