What number should be added to $3 x^{3} - 5 x^{2} + 6 x$ so that when resulting polynomial is divided by x - 3, the remainder is 8

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Solution

Dividing
$3 x^{3} - 5 x^{2} + 6 x$ by x−3.

For remainder to be 8 , (−18x+8) should be added to $3 x^{3} - 5 x^{2} + 6 x$ .

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