Solution
= Solution
Set $t=-x>0$. The coefficient formula gives
$$
(-1)^np_G(x)=\sum_{i=0}^{n-1}a_it^{n-i}.
$$
Every summand is nonnegative and the leading term is $t^n>0$, since $a_0=1$. Therefore
$$
\boxed{(-1)^np_G(x)>0\quad(x<0)}.
$$
= Solution
Set $t=-x>0$. The coefficient formula gives
$$
(-1)^np_G(x)=\sum_{i=0}^{n-1}a_it^{n-i}.
$$
Every summand is nonnegative and the leading term is $t^n>0$, since $a_0=1$. Therefore
$$
\boxed{(-1)^np_G(x)>0\quad(x<0)}.
$$