Subtract the sum of $({5 x}^{2} - 7 x + 4)$ and $(2 x - {5 x}^{3} + 1)$ from $({3 x}^{2} - 1 + 5 x)$ .

{5 x}^{3} + {11 x}^{2} - 5 x + 3

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5 x^{3} - 2 x^{2} + 10 x - 6

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{3 x}^{3} + {11 x}^{2} + 3 x + 5

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

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Solution

The correct option is B $5 x^{3} - 2 x^{2} + 10 x - 6$
$3 x^{2} - 1 + 5 x - [(5 x^{2} - 7 x + 4) + (2 x - 5 x^{3} + 1)]$
= $3 x^{2} - 1 + 5 x - [5 x^{2} - 5 x + 5 - 5 x^{3}]$
= $3 x^{2} - 1 + 5 x - 5 x^{2} + 5 x - 5 + 5 x^{3}$
= $- 2 x^{2} + 10 x - 6 + 5 x^{3}$
= $5 x^{3} - 2 x^{2} + 10 x - 6$

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