The area of a rectangle is given by the expression x2 + 5x + 4. if the length of one side is given by x + 2, what is the length of the other side?

Please use " ^ " to denote exponentiation.

Divide x^2 + 5x + 4 by x+2, using synth. div.:
     
-2 /    1       5       4
                  -2      -6
     
          1       3       -2

Strange outcome!  But if the area is truly x^2 + 5x + 4 and we divide that by side length x + 2, the quotient (result) is x + 3 with a remainder of -2.  Ensure that you have copied down the original problem correctly.