Solve x^6-8x^12=

$$x ^ { 6 } - 8 x ^ { 12 } =$$

Factor

$$\left(2x^{2}-1\right)\left(-4x^{4}-2x^{2}-1\right)x^{6}$$

Solution Steps

Factor out x^{6}.

$$x^{6}\left(1-8x^{6}\right)$$

Consider 1-8x^{6}. Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -8x^{6} and n divides the constant factor 1. One such factor is 2x^{2}-1. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -4x^{4}-2x^{2}-1,2x^{2}-1.

$$x^{6}\left(2x^{2}-1\right)\left(-4x^{4}-2x^{2}-1\right)$$

Evaluate

$$x^{6}-8x^{12}$$