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) 

Answer 2

Your answer would be 4x2 − 10x + 11+ 6 over quantity of 2 x plus 5.