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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (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
f%282%29=+%282%29%5E3-k%282%29%5E2%2B2

%282%29%5E3-k%282%29%5E2%2B2%7D=0
8-4k+2=0
4k=10
x= 10/4
k=5/2