Find the value of k if x-3 is a factor of k²x³-kx²+3kx-k.

Let, f (x) = k²x³-kx²+3kx-k

By factor theorem,

If (x – 3) is a factor of f (x) then f (3) = 0

k² (3)³ – k (3)² + 3 k (3) – k = 0

27k² – 9k + 9k – k = 0

k (27k – 1) = 0

k = 0 and (27k – 1) = 0

k = 0 and k =

Hence, (x – 3) is a factor of f (x) when k = 0 or k = .