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Addition and Subtraction of Algebraic Expression

What must be ...

Question

What must be added to $x^{3} + 3 x - 8$ to get $3 x^{3} + x^{2} + 6$ ?

A

2 x^{3} + x^{2} - 3 x + 14

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B

2 x^{2} + x^{2} + 14

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C

2 x^{3} + x^{2} - 6 x - 14

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D

None of these

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Solution

The correct option is D $2 x^{3} + x^{2} - 3 x + 14$
Let the polynomial to be added be $p$ .
$∴ x^{3} + 3 x - 8 + p = 3 x^{3} + x^{2} + 6$
$∴ p = 3 x^{3} + x^{2} + 6 - x^{3} - 3 x + 8$
$∴ p = 2 x^{3} + x^{2} - 3 x + 14$

Hence, Option A is correct.

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