Find the GCD of $(x^{4} - 1) and (x^{3} - 11 x^{2} + x - 11) .$

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Solution

$f (x) = x^{4} - 1$
$g (x) = x^{3} - 11 x^{2} + x - 11$
The degree of the polynomial f(x) is greater than g(x).

The remainder is $120 (x^{2} + 1),$ which is not equal to 0. So, we have to divide $x^{3} - 11 x^{2} + x - 11$ by $120 (x^{2} + 1)$ by leaving the remainder.

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