Question

What must be added to x - 3x² - 12x + 19 so that the result is exactly divisibly by x² + x - 6 ?​

Answer 1

Step-by-step explanation:

X² + 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) 

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