Factorize `1+x^4+x^8` – InterviewSolution

1.	Factorize `1+x^4+x^8`
Answer» `1 + x^4 + x^8` `= 1+ x^4 + x^8 + x^4 - x^4` using `x^8 = x^4x^4= (x^4)^2` `= 1 + 2x^4 + x^8 - x^4` using `(a+b)^2 = a^2 + 2ab + b^2` `(1)^2 + 21*(x^4) + (x^4)^2 - x^4` `= (x^4+1)^2 - x^4` `= (x^4 + 1)^2 - (x^2)^2` `= (x^4 + 1 - x^2)(x^4+1+x^2)` `= (x^4-x^2+1)(x^4+2x^2+1-x^2` `= (x^4-x^2+1)((x^2+1)^2-x^2)` `= (x^4 - x^2+1)(x^2-x+1)(x^2+x+1)` answer

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