What must be added to x³ – 3x²-12x+19 so that the result is exactly divisibly by x²+x – 6?​

Question

What must be added to x³ – 3x²-12x+19 so that the result is exactly divisibly by
x²+x – 6?​

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Eva 3 weeks 2021-10-05T05:18:23+00:00 1 Answer 0 views 0

Answers ( )

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    2021-10-05T05:19:24+00:00

    we add (2x + 5) 

    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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