Resolver x^16-1

$$x ^ { 16 } - 1$$

Faktorizatu

$$\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right)\left(x^{4}+1\right)\left(x^{8}+1\right)$$

Ebazpidea

Berridatzi x^{16}-1 honela: \left(x^{8}\right)^{2}-1^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

$$\left(x^{8}-1\right)\left(x^{8}+1\right)$$

Kasurako: x^{8}-1. Berridatzi x^{8}-1 honela: \left(x^{4}\right)^{2}-1^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

$$\left(x^{4}-1\right)\left(x^{4}+1\right)$$

Kasurako: x^{4}-1. Berridatzi x^{4}-1 honela: \left(x^{2}\right)^{2}-1^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

$$\left(x^{2}-1\right)\left(x^{2}+1\right)$$

Kasurako: x^{2}-1. Berridatzi x^{2}-1 honela: x^{2}-1^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

$$\left(x-1\right)\left(x+1\right)$$

Berridatzi faktorizatutako adierazpen osoa. Polinomio hauek ez daude faktorizatuta, ez baitute erro arrazionalik: x^{2}+1,x^{4}+1,x^{8}+1.

$$\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right)\left(x^{4}+1\right)\left(x^{8}+1\right)$$

Ebaluatu

$$x^{16}-1$$