Algorithm $x$ programmed by an "ace programmer" runs in time $2\mathrm{.}5n^4+3n^3+1\mathrm{.}4n+2$ for inputs of size $n$

$3$ points

in the worst case. Another algorithm $Y$ programmed by a novice for the same problem runsin time $2000n+10000$ for inputs of size $n$ in the worst case.

Please select the correct answers

For inputs of size $2,x$ is much faster than $Y.$

Algorithm $x$ is going to be much faster than $Y$ for all inputs.

Algorithm $x$ runs in time $(n^4)$

Algorithm $Y$ runs in time $O(n^2)$

Algorithm $Y$ is asymptotically faster than $x.$

It is possible for some input of size $100$ that algorithm $x$ is faster than algorithm $Y$