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The coefficient of $$x$$ in the expansion of $$\left(\sqrt{7}\,x^4 + \frac{13}{4}x^3 + x^2 + 2x - 1\right)^{2009}$$ is ___________
Correct Answer: 4018
A term in $$x^1$$ arises only by taking $$2x$$ from one of the 2009 factors and $$-1$$ from all the others. This can be done in 2009 ways, each giving $$2x(-1)^{2008} = 2x$$. So the coefficient of $$x$$ is $$2009 \times 2 = 4018$$.
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