Find the sum of the coefficients in the expansion of $(3x^2 + x -2)^{2017}$

Question

To find the sum of the coefficients in the given multinomial expansion, need take all powers of the coefficients, while the variable $x$ terms are ignored.

So, $(3x^2 + 1.x -2)^{2017}= (3 + 1 -2)^{2017} = 2^{2017}$

Request vetting, & any alternate approach too.

Answer 1

I agree, because, if $f(x) =(3x^2 + x -2)^{2017} =\sum_{k=0}^m a_kx^k $ (whatever $m$ might be), then $\sum_{k=0}^m a_k =\sum_{k=0}^m a_k(1)^k =f(1) =(3(1)^2 + 1 -2)^{2017} =2^{2017} $.