Hello.
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?
Binomial coefficients can be used to find the sum of polynomial coefficients, but each polynomial requires its own approach. You don't claim that the sum of coefficients of any polynomial is , do you?
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)?
Pascal's triangle works if you're expanding something like . If you have something else, like , you need both binomial coefficients and the factor. Basically, you can't say that the sum of coefficients is always .
On the other hand, P(1) gives you the sum of coefficients.