Question 820318
{{{f(x)=x^3-kx^2+kx+2}}}
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.<br>
And yes, you will divide. Synthetic division is easiest:
<pre>
2 |   1   -k     k  2
---        2  4-2k  8-2k
     --------------------
      1  2-k  4-k   10-2k
</pre>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).