Question : What is the HCF of (x6 + 1) and (x4 - 1)?
Option 1: 1
Option 2: (1 + x)
Option 3: (1 - x2)
Option 4: (1 + x2)
Correct Answer: (1 + x 2 )
Solution : Use : $(a^{3} + b^{3}) = (a + b)(a^{2}− ab + b^{2})$ $a^{2} + b^{2} = (a + b)(a − b)$ So, $x^{6} + 1 = (x^{2})^{3} + 1^{3}$ = $(x^{2} + 1)(x^{4} − x^{2} + 1)$ Now, $x^{4} − 1 = (x^{2} + 1)(x^{2} − 1)$ So, HCF $(x^{6} + 1, x^{4} − 1) = (x^{2} + 1)$ Hence, the correct answer is $x^{2} + 1$
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