The product of $(x^{2} + 3 x + 5)$ and $(x^{2} - 1)$ is

x^{4} + 3 x^{3} - 4 x^{2} - 3 x - 5

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x^{4} + 3 x^{3} + 4 x^{2} - 3 x - 5

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x^{4} + 3 x^{3} + 4 x^{2} + 3 x - 5

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none of these

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Solution

The correct option is B $x^{4} + 3 x^{3} + 4 x^{2} - 3 x - 5$
$(x^{2} + 3 x + 5) \times (x^{2} - 1)$
$= x^{2} \times x^{2} + 3 x \times x^{2} + 5 \times x^{2} + x^{2} x - 1 + 3 x \times - 1 + 5 x^{2} - 1$
$= x^{4} + 3 x^{3} + 5 x^{2} - x^{2} - 3 x - 5$
$= x^{4} + 3 x^{3} + 4 x^{2} - 3 x - 5$

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