# 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

$$a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0} { > \boldsymbol{=0}}$$

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?

• I suggest you read up on what a polynomial is. – dkaeae Jun 7 '19 at 7:00
• I'm voting to close this question as it is not about CS but rather about basic math terminology. – dkaeae Jun 7 '19 at 7:01

Yes, $$x^{100000000000}$$ is a polynomial. Your first quote gives an example; your second is the definition.