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Find the coefficient of x^(5) in the e...

Find the coefficient of ` x^(5)` in the expansion of ` ((2 + 3x + 4x^(2)))/(e^(x))`

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`(2 + 3x + 4x^(2))e^(-x)= (2 + 3x + 4x ^(2)) (1 - (x)/(1!) + (x^(2))/(2!)-(x^(3))/(3!) + (x^(4))/(4!) - (x^(5))/(5!) + ...oo)`
So coefficient of ` x^(5)` in expansion of ` ((2 + 3x + 4x^(2))/(e^(x)))`
` = 2xx(-(1)/(5!)) + 3 xx(1)/(4!) + 4(-(1)/(3!))`
= `(-2)/(120) + (3)/(24) - (4)/(6)`
` = - (1)/(60) + (1)/(8) - (2)/(3) = (-2 + 15 - 80)/(120)`
` = (-67)/(120)`
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