Solve 8x^2-27x^8

$$8 x ^ { 2 } - 27 x ^ { 8 }$$

Factor

$$x^{2}\left(3x^{2}-2\right)\left(-9x^{4}-6x^{2}-4\right)$$

Solution Steps

Factor out x^{2}.

$$x^{2}\left(8-27x^{6}\right)$$

Consider 8-27x^{6}. Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -27x^{6} and n divides the constant factor 8. One such factor is 3x^{2}-2. Factor the polynomial by dividing it by this factor.

$$\left(3x^{2}-2\right)\left(-9x^{4}-6x^{2}-4\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -9x^{4}-6x^{2}-4,3x^{2}-2.

$$x^{2}\left(3x^{2}-2\right)\left(-9x^{4}-6x^{2}-4\right)$$

Evaluate

$$x^{2}\left(8-27x^{6}\right)$$