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Question

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


A
x4+3x34x23x5
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B
x4+3x3+4x23x5
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C
x4+3x3+4x2+3x5
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D
none of these
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Solution

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

Mathematics

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