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

Question

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

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Brielle 3 weeks 2021-10-04T16:12:36+00:00 1 Answer 0 views 0

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    2021-10-04T16:14:35+00:00

    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:

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