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Addition and Subtraction of Algebraic Expression

What must be ...

Question

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

A

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

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B

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

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C

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

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D

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

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Solution

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

Let the unknown be $= y$

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

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

$x^{3} - 3 x^{2} + 5 x - 1$
$2 x^{3} + x^{2} - 4 x + 2$
$(-) (-) (+) (-)$
____________________
$- x^{3} - 4 x^{2} + 9 x - 3$

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

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