SOLUTION: Find k such that f(x)=x^3-kx^2+kx+2 has the factor x-2. I have no idea what this is and my final is due in a few hours! help me please! I know I have to divide by x-2 but I don't

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find k such that f(x)=x^3-kx^2+kx+2 has the factor x-2. I have no idea what this is and my final is due in a few hours! help me please! I know I have to divide by x-2 but I don't      Log On


   

Question 820318: Find k such that f(x)=x^3-kx^2+kx+2 has the factor x-2.
I have no idea what this is and my final is due in a few hours! help me please!
I know I have to divide by x-2 but I don't know how to do so or what to do after that.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3-kx%5E2%2Bkx%2B2
First of all, this is a polynomial, not a rational function (which has x in denominator(s)). Please post your problems in a relevant category.

And yes, you will divide. Synthetic division is easiest:
2 |   1   -k     k  2
---        2  4-2k  8-2k
     --------------------
      1  2-k  4-k   10-2k
Since x-2 is supposed to be a factor, then we should get a remainder of zero when we divide. The remainder we got, 10-2k, must then be zero:
10-2k = 0
Adding 2k:
10 = 2k
Dividing by 2:
5 = k
This is the value for k that makes x-2 a factor of f(x).