Solve 135x^2-5x^5

$$135 x ^ { 2 } - 5 x ^ { 5 }$$

Factor

$$5\left(x-3\right)x^{2}\left(-x^{2}-3x-9\right)$$

Solution Steps

Factor out 5.

$$5\left(27x^{2}-x^{5}\right)$$

Consider 27x^{2}-x^{5}. Factor out x^{2}.

$$x^{2}\left(27-x^{3}\right)$$

Consider 27-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 27 and q divides the leading coefficient -1. One such root is 3. Factor the polynomial by dividing it by x-3.

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

Rewrite the complete factored expression. Polynomial -x^{2}-3x-9 is not factored since it does not have any rational roots.

$$5x^{2}\left(x-3\right)\left(-x^{2}-3x-9\right)$$

Evaluate

$$135x^{2}-5x^{5}$$