Question

Please correct,if necessary, and simplify using long division: (-72-4x^2+8x^3-36x) devided by (x-3). My solution:

8x^2+20x+24
-------------------
8x^3-4x^2-36x-72
8x^3-24x^2
------------------
20x^2-36x-72
20x^2-60x
-----------------------
24x-72
24x-72
-------------------------

Answer 1

correct, the division was exact with no remainder.
the answer is 8x^2 + 20x + 24

synthetic division confirms it:

3 | 8 - 4 - 36 - 72
........ 24 .. 60 .. 72
.... 8..20 .. 24 ... 0

the 8, 20, 24 represents 8x^2 + 20x + 24
the 0 shows no remainder.