SOLUTION: Find k such that x+2 is a factor of x^3-kx^2+3x+7k

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Question 393704: Find k such that x+2 is a factor of x^3-kx^2+3x+7k
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
By the remainder theorem, we must have
%28-2%29%5E3+-+k%28-2%29%5E2+%2B+3%2A%28-2%29+%2B+7k+=+0.
<==> -8 - 4k - 6 + 7k = 0
<==> -14 + 3k = 0
==> 3k = 14
==> k = 14/3.