Question 6287
 2x^2+5xy-3y^2+3x+4y+k =0,
 Factoring the first three terms, we have
 (2x + 3y)(x + y) + 3x + 4y + k = 0
 Assume the left polynomial can be factored into 
  (2x + y+ a)(x + 3y+b) =  (2x + 3y)(x + y) + (a+2b)x + (3a+b)y + k
 Comparing the coefficients,we have
 k = ab and
 a+2b = 3 , 3a+b = 4 
 Solve the system for a,b: we have a = 1 and b = 1
 Hence, k = ab = 1 

 Plz check the answer by yourself.

 Kenny