x^2 + 1/x^2 - 11
= x^2 + 1/x^2 - 9 - 2
= (x^2 - 2 + 1/x^2) - 9 , using commutativity and associativity
= (x^2 - 2x * 1/x + 1/x^2) - 3^2, since x * 1/x = 1
= (x - 1/x)^2 - 3^2, using A^2 -2AB + B^2 = (A - B)^2
= (x - 1/x + 3)(x - 1/x -3), Ans. using A^2 - B^2 = (A + B)(A - B)
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