Solve 5x^2-10x^5+15x^2

$$5 x ^ { 2 } - 10 x ^ { 5 } + 15 x ^ { 2 }$$

Factor

$$10x^{2}\left(2-x^{3}\right)$$

Solution Steps

Factor out 5.

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

Consider x^{2}-2x^{5}+3x^{2}. Factor out x^{2}.

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

Consider 1-2x^{3}+3. Multiply and combine like terms.

$$-2x^{3}+4$$

Consider -2x^{3}+4. Factor out 2.

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

Rewrite the complete factored expression.

$$10x^{2}\left(-x^{3}+2\right)$$

Simplify. Polynomial -x^{3}+2 is not factored since it does not have any rational roots.

$$10\left(-x^{3}+2\right)x^{2}$$

Evaluate

$$20x^{2}-10x^{5}$$

Solution Steps

Combine 5x^{2} and 15x^{2} to get 20x^{2}.

$$20x^{2}-10x^{5}$$