Answer :

Let, f (x) = k2x- kx+ 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 or (27k – 1) = 0


k = 0 or k =


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

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