SOLUTION: Find k such that f(x)=x^3-kx^2+2 has the factor x-2. I have no idea how to even approach this problem. Perhaps I could use synthetic division? 2| 1 -k 0 2 2

Question 591565: Find k such that f(x)=x^3-kx^2+2 has the factor x-2.
I have no idea how to even approach this problem.
Perhaps I could use synthetic division?
2| 1 -k 0 2
2 4-2k 8-4k
----------------
1 2-k 4-2k 10-4k
x^2+(2-k)x^2+(4-2k)x+10-4k
Well, that was a disaster.
Any help?

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
f(x)=x^3-kx^2+2 has the factor x-2.

The factor is x-2
2 is the zero of the function

8-4k+2=0
4k=10
x= 10/4
k=5/2

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