$What must be added to (x^{3} + 3 x - 8) to obtain (3 x^{3} + x^{2} + 6) ?$

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Solution

Let a polynomial P must be added.
Therefore, according to the question,

$P + (x^{3} + 3 x - 8) = (3 x^{3} + x^{2} + 6) \Rightarrow P = (3 x^{3} + x^{2} + 6) - (x^{3} + 3 x - 8) \Rightarrow P = (3 - 1) x^{3} + x^{2} - 3 x + (6 - (- 8)) \Rightarrow P = 2 x^{3} + x^{2} - 3 x + 14$

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