Question

Let f(x) = 8x3 - 28x + 61 and g(x) = 2x + 5. Find f(x) / g(x)

Answer 1

This is a division of polynomials

8x^3 - 28x + 61 | 2x + 5
-----------------------
- 8x^3 - 20x^2 4x^2 - 10x + 11x
---------------------------------
0 - 20x^2 - 28x + 61
+20x^2 +50x
------------------------
0 +22x +61
-22x -55
----------------
6

Then, the division is not exact and the result is 4x^2 - 10x + 11x with remainder 6, or:

4x^2 - 10x + 11x + [ 6/ ( 2x + 5)