Cyclic Polynomials - Factoring
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Factorize .
Let the above polynomial equal . We know that is a cyclic polynomial because .
Note that . By the factor theorem, we can say that is a factor of . If is a factor of , then it must be true that is also a factor of because is cyclic.
The degree of is 3. Also, has a degree of 3. Thus, the factored result of is equal to . If we let and solve the equation , we can see that and our final factored result is .