Question

How do i do this using long division? This is part of a Partial Fractions Question. Please help, thanks!

(x^3) / (x^3 - 2x^2 + 3x - 18)
I tried using long division, but I could only get a quotient of 1, and a remainder of 2x^2 - 3x + 18

Did i do something wrong?

Answer 1

One does not use polynomial long division to apply the method of partial fractions. Try factoring x^3 - 2x^2 + 3x - 18 instead. The factors are (x-3)and (x^2 +x -6).

The next step is, I believe to express your ratio in terms of
C/(x-3) + (Ax + B)/(x^2 +x -6).

where A, B and C are constants. There should be three values that work.

Answer 2

Change (x^2 +x -6) to (x^2 +x +6)