Solve x^7-x^2

$$x ^ { 7 } - x ^ { 2 }$$

Factor

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

Solution Steps

Factor out x^{2}.

$$x^{2}\left(x^{5}-1\right)$$

Consider 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.

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

Rewrite the complete factored expression. Polynomial x^{4}+x^{3}+x^{2}+x+1 is not factored since it does not have any rational roots.

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

Evaluate

$$x^{2}\left(x^{5}-1\right)$$