Which polynomial should be subtracted from $y^{3} + 2 y^{2} + 5 y - 1$ to get $2 y^{2} + 12$ ?

y^{3} + 5 y - 13

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y^{3} + y - 1

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5 y - 3

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y^{3} - y - 14

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Solution

The correct option is A $y^{3} + 5 y - 13$
The bigger polynomial is $y^{3} + 2 y^{2} + 5 y - 1$
Let one polynomial be $p$ .
Therefore,
$y^{3} + 2 y^{2} + 5 y - 1 - p = 2 y^{2} + 12$
$=> y^{3} + 2 y^{2} + 5 y - 1 - 2 y^{2} - 12 = p$
$= y^{3} + 5 y - 13$
Therefore,
The polynomial to be subtracted is $y^{3} + 5 y - 13$

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