If $\frac{f(x^2)}{f(x)}=1+x+x^2+\ldots+x^7$ then what is $f(x)$?
Solution 1:
Simply use $$x^n+1=\frac{x^{2n}-1}{x^n-1}$$ for each factor of your decomposition $$(x+1)(x^2+1)(x^4+1).$$
If $\frac{f(x^2)}{f(x)}=1+x+x^2+\ldots+x^7$ then what is $f(x)$?
Solution 1:
Simply use $$x^n+1=\frac{x^{2n}-1}{x^n-1}$$ for each factor of your decomposition $$(x+1)(x^2+1)(x^4+1).$$