If (x-1)^{3} is a factor of x^{4}+\alpha x^{3}+\beta x^{2}+\gamma x-1, then the other factor will be :

Explanation

Let the other factor be (x-k). Then x^4 + \alpha x^3 + \beta x^2 + \gamma x - 1 = (x-1)^3(x-k). Comparing constant terms, (-1)^3 \times (-k) = -1, which gives k = -1. The other factor is x - (-1) = x+1.

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