what is 14xsquared + 3x - 5 divided by 2x+5?

14x^2 + 3x  - 5     (factor)

(7x +5) (2x - 1)      thus.....2x + 5 doesn't divide this equally......so we have

                  7x     - 16

2x + 5     14x^2  + 3x -  5

               14x^2 + 35x

              ----------------------

                          -32x   - 5

                          -32x  - 80

                           -----------

                                    75

=    (7x - 16)    Remainder  (75) / (2x + 5)

You have set that algebraic division out really nicely Chris