Coefficient trouble?

Notice that there are 18 terms in the given problem. Therefore, an $x^{17}$ term would have to be multiplied out by 17 of the expansions to give $x^{17}$ , while the final one provides its numeric value.

The terms that would come are : $-1x^{17} -2x^{17} -3x^{17} .... - 18x^{17}$ $-(1+2+3+...17+18) x^{17}$ $-171x^{17}$

Let p(x) = above expression , then by Vieta's Formula , coefficient of x^17 = -(sum of roots of polynomial) = -(1+2+3....+18) = -18*19/2 = -171