# Thread: Long Division in this Problem

1. ## Long Division in this Problem

I'm doing partial fractions and honestly can't figure out how to divide x^3 by x^2+5x+6 using long division. Could somebody go through it step by step and remind me?

2. Originally Posted by fattydq
I'm doing partial fractions and honestly can't figure out how to divide x^3 by x^2+5x+6 using long division. Could somebody go through it step by step and remind me?
Code:
           x  -  5
--------------
x^2+5x+6 | x^3
x^3 + 5x^2 + 6
-----------------
-5x^2        - 6
-5x^2 - 25x - 30
------------------
25x + 24
$\frac{x^3}{x^2+5x+6} = x - 5 + \frac{25x + 24}{x^2+5x+6}$

3. I don't understand how you didn't carry the 6x in the second line "inside" your long division?

4. sorry, my mistake ...

Code:
           x  -  5
--------------
x^2+5x+6 | x^3
x^3 + 5x^2 + 6x
-----------------
-5x^2  - 6x
-5x^2 - 25x - 30
------------------
19x + 30
$\frac{x^3}{x^2+5x+6} = x - 5 + \frac{19x + 30}{x^2+5x+6}$

better?

5. Yeah thanks a lot