Solve 7x^5-7x

$$7 x ^ { 5 } - 7 x$$

Factor

$$7x\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right)$$

Solution Steps

Factor out 7.

$$7\left(x^{5}-x\right)$$

Consider x^{5}-x. Factor out x.

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

Consider x^{4}-1. Rewrite x^{4}-1 as \left(x^{2}\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Rewrite the complete factored expression. Polynomial x^{2}+1 is not factored since it does not have any rational roots.

$$7x\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right)$$

Evaluate

$$7x\left(x^{4}-1\right)$$