Resolver x^7-x

$$x ^ { 7 } - x$$

Faktorizatu

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

Ebazpidea

Deskonposatu x.

$$x\left(x^{6}-1\right)$$

Kasurako: x^{6}-1. Berridatzi x^{6}-1 honela: \left(x^{3}\right)^{2}-1^{2}. Kuboen diferentzia faktorizatzeko, erabili a^{2}-b^{2}=\left(a-b\right)\left(a+b\right) araua.

$$\left(x^{3}-1\right)\left(x^{3}+1\right)$$

Kasurako: x^{3}-1. Berridatzi x^{3}-1 honela: x^{3}-1^{3}. Kuboen diferentzia faktorizatzeko, erabili a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right) araua.

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

Kasurako: x^{3}+1. Berridatzi x^{3}+1 honela: x^{3}+1^{3}. Kuboen batura faktorizatzeko, erabili a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right) araua.

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

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

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

Ebaluatu

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