Which of the following expressions simplify to n$^2$ after removing lower$-$order terms and constant factors? Select all that apply.

$($a$)$

$4$n$^2+3$n

$($b$)$

n$^2(3+$ log n$)$

$($c$)$

$4$n $($n $+3)$

$($d$)$

$6$n $($log n$)^3+$ n$^2+4$n

$($e$)$

n $($sqrt n$)($log n$)+$ sqrt n