Question

what should be added so that x cube minus 3 x square - 12 x + 19 is exactly divisible by X square + X - 6 ​

Answer 1

Answer:

vx² + x -6 ) x³ - 3x² -12x  + 19 ( x -4

               x³ + x² -6x

   --------------------------------

             -4x² -6x + 19 

             -4x²-4x + 24 

-------------------------------------

                  -2x - 5 

hence ,

  x³ - 3x² -12x + 19 = (x² +x - 6)(x - 4) -(2x + 5)

   x³ - 3x² -12x + 19  + (2x + 5)   = (x² + x - 6)(x - 4)

hence if we add (2x + 5) 

Step-by-step explanation: