What should be added to $(3 x^{3} - 2 x^{2} + 3 x - 1)$ to get $(x^{3} + 2 x^{2} - 6 x + 5) ?$ .

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Solution

Let $y$ be the quantity being added.
$∴ (3 x^{3} - 2 x^{2} + 3 x - 1) + y = x^{3} + 2 x^{2} - 6 x + 5$
$∴ y = x^{3} + 2 x^{2} - 6 x + 5 - (3 x^{3} - 2 x^{2} + 3 x - 1)$
$∴ y = - 2 x^{3} + 4 x^{2} - 9 x + 6$
Hence, the quantity to be added is $- 2 x^{3} + 4 x^{2} - 9 x + 6$ .

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