If an algorithm's best case needs $25$n $2+3$n $+5$ primitive operations,

a$)$ the algorithm's worst case may do $\_\_\_\_\_$ primitive operations.

A$.$ f$($n$)=15$n $+7$

B$.$ f$($n$)=$ n $3$

b$)$ Show the range of value of n that satisfy f$($n$)>=25$n$2+3$n$+5.$ If you find it$$s difficult to prove it mathematically. You may need to use a piece of code to have a test and attach the data you collected.