Solve x^5-1^5

$$x ^ { 5 } - 1 ^ { 5 }$$

Factor

$$\left(x-1\right)\left(x^{4}+x^{3}+x^{2}+x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{5}-1$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -1 and q divides the leading coefficient 1. One such root is 1. Factor the polynomial by dividing it by x-1. Polynomial x^{4}+x^{3}+x^{2}+x+1 is not factored since it does not have any rational roots.

$$\left(x-1\right)\left(x^{4}+x^{3}+x^{2}+x+1\right)$$

Evaluate

$$x^{5}-1$$

Solution Steps

Calculate 1 to the power of 5 and get 1.

$$x^{5}-1$$