Solve 2x^2-16x^2y^3

$$2 x ^ { 2 } - 16 x ^ { 2 } y ^ { 3 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(x^{2}-8x^{2}y^{3}\right)$$

Consider x^{2}-8x^{2}y^{3}. Factor out x^{2}.

$$x^{2}\left(1-8y^{3}\right)$$

Consider 1-8y^{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 -8. One such root is \frac{1}{2}. Factor the polynomial by dividing it by 2y-1.

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

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

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

Evaluate

$$2x^{2}\left(1-8y^{3}\right)$$