Question

I need help with this

Answer 1

First lets invert the divisor and chane to a multuplication:-
       x + 5                     2x^2 - 7x - 4
-----------------        *   --------------------
2x^2 + 3x + 1           3x^2 + 18x + 15

Now we can factor  the 3 trinomials:-
      x + 5                   (2x + 1)(x - 4)
 --------------         *   ------------------
(2x + 1)(x + 1)        3(x + 5)(x + 1)

Now we simplify because (2x + 1) and (x + 5) are common to top and bottom:-
            1             *        x - 4
=  -------------           ------------
       x + 1              3( x + 1)

=       x - 4
    --------------
     3(x + 1^2