SOLUTION: For what value of k is x^3 - 2kx^2 + 3x + k exactly divisible by x-2

Algebra ->  Test -> SOLUTION: For what value of k is x^3 - 2kx^2 + 3x + k exactly divisible by x-2      Log On


   

Question 1183611: For what value of k is x^3 - 2kx^2 + 3x + k exactly divisible by x-2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
When you divide that polynomial P%28x%29=x%5E3+-+2kx%5E2+%2B+3x+%2B+k by x-2 the quotient is Q%28x%29 , another polynomial of degree 2.
In other words P%28x%29=%28x-2%29%2AQ%28x%29 for every value of x
and so for x=2 we have P%282%29=%282-2%29%2AQ%28x%29=0%2AQ%28x%29=0 .
So,
2%5E3+-+2k2%5E2+%2B+3%2A2+%2B+k=0
8+-+2k%2A4+%2B+6+%2B+k=0
14+-+8k+%2B+k=0
14+-+7k=0 --> highlight%28k=14%2F7%29