Solve 2x^4+x^2+4x^3+2x

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

Factor

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

Solution Steps

Factor out x.

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

Consider 2x^{3}+x+4x^{2}+2. Do the grouping 2x^{3}+x+4x^{2}+2=\left(2x^{3}+x\right)+\left(4x^{2}+2\right), and factor out x in the first and 2 in the second group.

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

Factor out common term 2x^{2}+1 by using distributive property.

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

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

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

Evaluate

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