please provide detailed solution of p20 of ex3.3 from numerical analysis burden and faires 9th edition pic attached

Show that f(n+1) (E (x) ) f[xo, X1 , . . . , Xn, X] = (n + 1)! for some &(x). [Hint: From Eq. (3.3), f( n+1)(8(x) ) f (x) = Pn(x) + (x - XO) . . . ( x - Xn). (n + 1)! Considering the interpolation polynomial of degree n + 1 on x0, x1, . . ., xn, x, we have f (x) = Pn+1(x) = Pn(x) + f[xo, X1 , . . ., Xn, x] (x - XO) . . . (x - Xn).]