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If $f (x) = x^{4} + 3 x^{2} - 6 x - 2$ , then the coefficient of $x^{3}$ in $f (x + 1)$ is

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Detailed Solution

f (x + 1) = {(x + 1)}^{4} + 3 {(x + 1)}^{2} - 6 (x + 1) - 2

$= x^{4} +^{4} C_{3} x^{3} +^{4} C_{2} x^{2} +^{4} C_{1} x +^{4} C_{4} + 3 (x^{2} + 2 x + 1) - 6 x - 6 - 2$

coefficient of $x^{3}$ $=^{4} C_{3} =^{4} C_{1} = 4$

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