Question

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

Answer 1

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.