The expression $(x^{2} + 2 x - 3) (2 x + 5) - (x + 1) (x - 1) (x + 3)$ . After solving can be expressed in the form $a x^{3} + b x^{2} + c x + d$ , where the value of $a + b + c + d$ is:

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Solution

The correct option is A 0

$(x^{2} + 2 x - 3) (2 x + 5) - (x + 1) (x - 1) (x + 3)$
$=$ $(2 x^{3} + 4 x^{2} - 6 x + 5 x^{2} + 10 x - 15) - ((x^{2} - 1) (x + 3))$
$=$ $2 x^{3} + 4 x^{2} - 6 x + 5 x^{2 +} + 10 x - 15 - (x^{3} - x + 3 x^{2} - 3)$
$=$ $2 x^{3} + 4 x^{2} - 6 x + 5 x^{2 +} + 10 x - 15 - x^{3} + x - 3 x^{2} + 3$
$=$ $2 x^{3} - x^{3} + 4 x^{2} + 5 x^{2} - 3 x^{2} - 6 x + 10 x + x - 15 + 3$
$=$ $x^{3} + 6 x^{2} + 5 x - 12$
Compare equation $x^{3} + 6 x^{2} + 5 x - 12$ with equation $a x^{3} + b x^{2} + c x + d$
We get $a = 1, b = 6, c = 5$ and $d = - 12$
Then $a + b + c + d = 1 + 6 + 5 - 12 = 0$

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