Sum these coefficients

Algebra Level 3

Determine the sum of all coefficients of the polynomial

\[f(x) = (3x^3-3x-1)^{38}\cdot(2x+1)^4\cdot(x^4-3x^2+5x-2)^{77}. \]

Details and assumptions

After expanding out the expression for \(f(x)\) given in the problem, one will arrive at a formula that looks like \(f(x)=a_n x^n+a_{n-1}x^{n-1}+\dotsc+a_1 x+a_0\), where \(a_0,a_1,a_2,\dotsc,a_n\) are numbers. The sum of coefficients of \(f(x)\) is \( a_n + a_{n-1} + \ldots + a_1 + a_0 \).


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