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Hcf of x^2-1 & ax^3-b(x+1) is (x-1) hence (x-1) is a factor of both polynomials
on dividing ax^3-b(x+1) from (x-1) we get remainder a-2b 
(x-1) to be factor of ax^3-b(x+1) remainder should be zero 
a-2b = 0 
a = 2b
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