Solve x^3-x^6

$$x ^ { 3 } - x ^ { 6 }$$

Factor

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

Solution Steps

Factor out x^{3}.

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

Consider 1-x^{3}. 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.

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

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

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

Evaluate

$$x^{3}-x^{6}$$