Which polynomial should be added to $2 x^{4} - 3 x^{2} + 5 x + 8$ to get $2 x^{2} - 5 x + 4$ ?

x^{3} + 5 x^{2} - x

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2 x^{5} + x^{2} - 10 x - 9

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- 2 x^{4} + 5 x^{2} - 1

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- 2 x^{4} + 5 x^{2} - 10 x - 4

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Solution

The correct option is D $- 2 x^{4} + 5 x^{2} - 10 x - 4$
The sum of two polynomials= $2 x^{2} - 5 x + 4$
Let one polynomial be $p$ .
Therefore,
$2 x^{4} - 3 x^{2} + 5 x + 8 + p = 2 x^{2} - 5 x + 4$
$=> p = 2 x^{2} - 5 x + 4 - 2 x^{4} + 3 x^{2} - 5 x - 8$
$=> p = - 2 x^{4} + 5 x^{2} - 10 x - 4$
The polynomial to be added is $- 2 x^{4} + 5 x^{2} - 10 x - 4$

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