What is the coefficient of x in (x^4 + x^3 + x^2 + x + 1)^5?
There is only one way we get x: multiplying 1 by x.
Thus, we look only at the x+1 terms.
(x+1)^5, and by pascal's triangle rules, we have that this expression is equal to \(x^5 + 5 x^4 + 10 x^3 + 10 x^2 + 5 x + 1.\)
The answer is 5.
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