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Addition and Subtraction of Polynomials

What should b...

Question

What should be added to $1 - x + x^{2} - 2 x^{3}$ to get $x^{3}$ ?

A

x^{3} - x^{2} + x - 1

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B

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

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C

3 x^{3} - x^{2} + x - 1

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D

3 x^{3} + x^{2} - x - 1

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Solution

The correct option is C $3 x^{3} - x^{2} + x - 1$
Let, the term to be added be y.
$\Rightarrow 1 - x + x^{2} - 2 x^{3} + y = x^{3}$
$\Rightarrow y = x^{3} - (1 - x + x^{2} - 2 x^{3})$
$= x^{3} - 1 + x - x^{2} + 2 x^{3}$
$= 3 x^{3} - x^{2} + x - 1$ .
Hence, $y$ = $3 x^{3} - x^{2} + x - 1$ .

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