NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Give as good a big$-$O estimate as possible for each of the following functions.

f$($n$)=($n$!+2$n$)($n$3+$ log$($n$2+1))$

Multiple Choice

O$($n$3$ n$!)$

O$($n$32$n$)$

O$($n$!)$

O$($n$3)$