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Addition and Subtraction of Algebraic Expressions

What has to b...

Question

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

A

3 - 8

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B

- 2x + 14

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C

x + 6

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D

2x + 14

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Solution

The correct option is B
- 2x + 14

Let the term which is to be added to $x^{2} + 3 x - 8$ be $P$ .

Then, $(x^{2} + 3 x - 8) + P = x^{2} + x + 6$

$⟹ P = (x^{2} + x + 6) - (x^{2} + 3 x - 8)$
$= x^{2} + x + 6 - x^{2} - 3 x + 8$
$= - 2 x + 14$
So, $- 2 x + 14$ is to be added to (\x^2 + 3x - 8\) to get (\x^2 + x + 6\).

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