The correct option is C x+1x
We can use the identity a2+2ab+b2=(a−b)2 we can simplify the expression as follows.
x2+1x2+2−2x−2x
=(x2+1x2+2)−2(x+1x)
=(x+1x)2−2(x+1x)
=(x+1x)(x+1x−2)
Thus, the factors of x2+1x2+2−2x−2x are
(x+1x) and (x+1x−2).
Among these (x+1x) is there in options.