SOLUTION: Find k so that x+2 is a factor of x^3 - kx^2 + 3x + 7k Can you please help me out? Thanks so much in advance:)

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Question 825879: Find k so that x+2 is a factor of x^3 - kx^2 + 3x + 7k
Can you please help me out? Thanks so much in advance:)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When I do the division +%28+x%5E3+-+kx%5E2+%2B+3x+%2B+7k++%29+%2F+%28+x+%2B+2+%29+,
I get +x%5E2+-+%28+k%2B2+%29%2Ax+%2B+2k+%2B+7+ with a remainder of
+%28+3k+-+14+%29%2F%28+x%2B2+%29+ I want to make the remainder zero, so
+3k+-+14+=+0+
+3k+=+14+
+k+=+14%2F3+
-------------
check:
+%28x+%2B+2+%29%2A%28+x%5E2+-+%28+k%2B2+%29%2Ax+%2B+2k+%2B+7+%29+
+%28x+%2B+2+%29%2A%28+x%5E2+-+%28+14%2F3%2B2+%29%2Ax+%2B+2%2A%2814%2F3%29+%2B+7+%29+
+%28x+%2B+2+%29%2A%28+x%5E2+-+%28+20%2F3+%29%2Ax+%2B+28%2F3+%2B+21%2F3+%29+
+%28x+%2B+2+%29%2A%28+x%5E2+-+%28+20%2F3+%29%2Ax+%2B+49%2F3+%29+
This should equal the original equation with +k+=+14%2F3+- you can finish