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 = .