What must be added to $x^{2} + 5 x - 6$ to get $x^{3} - x^{2} + 3 x - 2$ ?

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

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

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

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Solution

The correct option is D $x^{3} - 2 x^{2} - 2 x + 4$
Let the polynomial to be added be $p (x)$
$∴ x^{2} + 5 x - 6 + p (x) = x^{3} - x^{2} + 3 x - 2$
$∴ p (x) = x^{3} - x^{2} - x^{2} + 3 x - 5 x - 2 + 6$
$∴ p (x) = x^{3} - 2 x^{2} - 2 x + 4$

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