Long Division

 

         ______x + (7-k)

x+k |  x^2 + 7x        +12

          x^2  +kx          ___

                  7x-kx     +12

                  7x-kx     + 7k - k^2           for no remainder     7k-k^2 must = 12

                                                                                          k^2 -7k+12 =0

                                                                                          (k-3)(k-4) = 0    k = 4 or 3

 

 

(x+3 )(x+4) = x^2 +7x + 12    check!