$3\mathrm{.}4$ An alternate method for computing PN$($x$)$ is to write$$PN$($x$)=$ cl $+$ c$2$x $+$ c$3$x$2++$ cNxN$-$l $.$Then the interpolation conditions, PN$($xi$)=$ fi for$1<$ i $<$ N$,$ yield a system of N equations in the N$$unknowns c$1,$ c$2,...,$ cN that can be solved using the$$codes Factor$/$Solve$.$ Unfortunately, there are two difficulties$$with this method: $(1)$ it is expensive $($N$3/3$multiplications$),$ and $(2)$ the coefficient matrix can be$$very ill$-$conditioned.$($a$)$ Implement this algorithm.