Solve -2v^2-2v^4-4v^5

$$- 2 v ^ { 2 } - 2 v ^ { 4 } - 4 v ^ { 5 }$$

Factor

$$2\left(v+1\right)v^{2}\left(-2v^{2}+v-1\right)$$

Solution Steps

Factor out 2.

$$2\left(-v^{2}-v^{4}-2v^{5}\right)$$

Consider -v^{2}-v^{4}-2v^{5}. Factor out v^{2}.

$$v^{2}\left(-1-v^{2}-2v^{3}\right)$$

Consider -1-v^{2}-2v^{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 -2. One such root is -1. Factor the polynomial by dividing it by v+1.

$$\left(v+1\right)\left(-2v^{2}+v-1\right)$$

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

$$2v^{2}\left(v+1\right)\left(-2v^{2}+v-1\right)$$

Evaluate

$$-4v^{5}-2v^{4}-2v^{2}$$