Write f(x) in the form (x-k)q(x)+r, given that k=-2. f(x)=3x^4+4x^3-10x^2+15

You may perform the division using either long division or synthetic division.  Any preference?

I used synthetic div. with -2 as the divisor:

     
-2  /  3   4   -10   0   15
             -6     4   12  -24
       
        3    -2   -6    12   -9

In factored form, with remainder, we then have:

   (x+2)(3x^3 - 2x^2 - 6x + 12)   remainder -9

If you need clarification of any part of this solution, let me know.

50.1 terminates meaning it doesn't go on forever, that means it is a rational number