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(A) The sum of the coefficients in the expansion of a polynomial $P(x, y, z)$ is found by setting all variables equal to $1$.For the expansion $(x - 2

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$35$

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(A) The sum of the coefficients in the expansion of a polynomial $P(x, y, z)$ is found by setting all variables equal to $1$.For the expansion $(x - 2y + 3z)^n$,the sum of coefficients is $(1 - 2 + 3)^n = 2^n$.Given $2^n = 128$,we have $2^n = 2^7$,which implies $n = 7$.The expansion of $(1 + x)^7$ is given by $\sum_{k=0}^{7} {^7C_k} x^k$.The coefficients are ${^7C_0}, {^7C_1}, {^7C_2}, {^7C_3}, {^7C_4}, {^7C_5}, {^7C_6}, {^7C_7}$.The greatest coefficient is the middle term,which is ${^7C_3}$ or ${^7C_4}$.Calculating the value: ${^7C_3} = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} = 35$.

If the sum of the coefficients in the expansion of $(x - 2y + 3z)^n$,$n \in N$ is $128$,then the greatest coefficient in the expansion of $(1 + x)^n$ is

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