a$.$ Design a brute$-$force algorithm for computing the value of a polynomialp$($x$)=$ an x n $+$ a n$1$x n$1+...+$ a$1$x $+$ a$0$at a given point x$0$ and determine its worst$-$case efficiency class.b$.$ If the algorithm you designed is in $($n$2),$ design a linear algorithm for thisproblem.c$.$ Is it possible to design an algorithm with a better$-$than$-$linear efficiency forthis problem?