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Given p(x) = x4 - 3x2 + 4x +1
and y(x) = x2 - x = 1
=> y(x) = x2 -x-1 = 0
Now p(x)/y(x) = (x4 - 3x2 + 4x +1)/(x2 -x-1)
So the remainder is 4x