Question

6) What should be added in the polynomial x 3

- 3x 2 + 6x -15 so that it is

completely divisible by x - 3.​

Answer 1

Sol:

Given polynomial x3 - 3x2 - 12x + 19

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

x3 + x2 - 6x ( substract)

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

- 4x2 - 6x + 19

- 4x2 - 4x + 24 ( substract)

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

- 2x - 5

Here remainder is - 2x - 5 . 2x + 5 must be added to x3 - 3x2 - 12x + 19, so that result is exactly divisible by x2 + x - 6

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