What must be subtracted from or added to 6 x4-7 x3-26 x2-25 x-25 so that it may be exactly divisible by 3 x2-x-4 -

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Division Algorithm for a Polynomial

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Question

What must be subtracted from or added to 6x⁴+7x³-26x²-25x+25 so that it may be exactly divisible by 3x²-x+4?

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6 x^{4} + 13 x^{3} + 13 x^{2} + 30 x + 20

3 x^{2} + 2 x + 5

6 x^{4} - x^{3} + 3 x^{2} + 4 x - 2

3 x^{2} - 2 x + 4

14 x^{2} + 13 x - 15

7 x - 4

p^{2} - 6 p + 7

(p - 1)

x^{3} + 13 x^{2} + 35 x + 25

x^{2} + 11 x + 10

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