What must be subtracted from $(x^{3} - 3 x^{2} + 5 x - 1)$ to get $(2 x^{3} + x^{2} - 4 x + 2)$ ?

$- x^{3} + 4 x^{2} + 9 x - 3$

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

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$- x^{3} - 4 x^{2} + 9 x - 9$

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$- x^{3} - 4 x^{2} + 9 x - 3$

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Solution

The correct option is D
$- x^{3} - 4 x^{2} + 9 x - 3$

Let the expression to be subtracted be $y$ .

Hence,
$(x^{3} - 3 x^{2} + 5 x - 1) - y = 2 x^{3} + x^{2} - 4 x + 2$

On rearranging the terms,
$y = (x^{3} - 3 x^{2} + 5 x - 1) - (2 x^{3} + x^{2} - 4 x + 2)$

$y = x^{3} - 3 x^{2} + 5 x - 1 - 2 x^{3} - x^{2} + 4 x - 2$

$y = x^{3} - 2 x^{3} - 3 x^{2} - x^{2} + 5 x + 4 x - 1 - 2$

$\Rightarrow y = - x^{3} - 4 x^{2} + 9 x - 3$

So we have to subtarct $(- x^{3} - 4 x^{2} + 9 x - 3)$ to get the required value.

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