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Question

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

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Solution

Let be the given polynomial.

By the factor theorem,

(x − 3) is a factor of f(x) if f (3) = 0

Therefore,


27k2-9k+9k-k=027k2-k=0k27k-1=0k=0 or k=127

Hence, the value of k is 0 or .


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