Analyze the complexity for computing a polynomial f $($x$)$ of degree n for a given x value using a brute$-$force approach and the Horner$$s approach, respectively. A bruteforce approach is to compute each term in the polynomial and add them together.

f$($x$)=$ a$\_$nx$^$n $+$ a$\_($n $-1)$x$*($n $-1)+$ a$\_($n $-2)$x$^($n $-2)+...+$ a$\_1$x$^1+$ a$\_0$