Given that f(x) =x^3-kx^2-2x+1 gives a remainder k when divided by x-k,find the value of k

Answer 1

a little synthetic division reveals that

f(x) = (x-k)(x^2-2) + (1-2k)
so, 1-2k = k
k = 1/3

f(x) = x^3 - 1/3 x^2 - 2x + 1
= (x-1/3)(x^2-2) + 1/3

Answer 2

not valid