is $x^{100000000000}$ a "polynomial time"? per this post 


  $t = x^2$ means the problem is solvable in "Polynomial" time.


per this post


  in the form
  
  $$a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0} {
&gt; \boldsymbol{=0}}$$
  
  plug in $n=100000000000$ with $a_n=1$ and $a_k=0$ for all $k \neq n$ 
  
  then we see that $x^{100000000000}$ is a polynomial
  
  it doesn't matter if its 2, 3, or a billion, as long as the n is a finite number


in this context, does $t = x^{100000000000}$ still mean the problem is solvable in "Polynomial" time?
Yes, $x^{100000000000}$ is a polynomial. Your first quote gives an example; your second is the definition.