Find the product of $(2 x - 5 + 1) (4 x^{3} + 2 x^{2} - 1)$ .

12 x^{4} - 8 x^{3} - 8 x^{2} - 2 x + 4

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12 x^{4} + 16 x^{3} - 8 x^{2} - 2 x + 4

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12 x^{4} - 16 x^{3} - 8 x^{2} + 2 x + 4

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12 x^{4} - 16 x^{3} - 8 x^{2} - 2 x + 4

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Solution

The correct option is D $12 x^{4} - 16 x^{3} - 8 x^{2} - 2 x + 4$
$(2 x - 5 + 1) (4 x^{3} + 2 x^{2} - 1)$
Multiply the coefficients and add the exponents of the variable.
$=$ $2 x .4 x^{3} + 2 x .2 x^{3} - 2 x .1 - 5.4 x^{3} - 5.2 x^{2} + 5 + 4 x^{3} + 2 x^{2} - 1$
$=$ $8 x^{4} + 4 x^{4} - 2 x - 20 x^{3} - 10 x^{2} + 4 + 4 x^{3} + 2 x^{2}$
$=$ $12 x^{4} - 16 x^{3} - 8 x^{2} - 2 x + 4$

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