What should be added to $x^{2} + 6 x - 18$ to get $3 x^{3} + x^{2} + 16$ ?

3 x^{3} - 6 x - 2

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

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3 x^{3} - 4 x - 2

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

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Solution

The correct option is A $3 x^{3} - 6 x - 2$
Let the expression to be added be 'y',
$(x^{2} + 6 x - 18) + y = 3 x^{3} + x^{2} + 16$
$y = (3 x^{3} + x^{2} + 16) - (x^{2} + 6 x - 18)$
Grouping the like terms together we get,
$y = 3 x^{3} + (x^{2} - x^{2}) - 6 x + (16 - 18)$
$\Rightarrow$ $y = 3 x^{3} - 6 x - 2$
Hence, the expression to be added is $3 x^{3} - 6 x - 2$ .

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