Solve 4x^2-8x^4-2x-4*x^6+2x^2+2{x}^7

$$4 { x }^{ 2 } -8 { x }^{ 4 } -2x-4 \times { x }^{ 6 } +2 { x }^{ 2 } +2 { x }^{ 7 }$$

Factor

$$2x\left(x^{6}-2x^{5}-4x^{3}+3x-1\right)$$

Solution Steps

Factor out 2.

$$2\left(2x^{2}-4x^{4}-x-2x^{6}+x^{2}+x^{7}\right)$$

Consider 2x^{2}-4x^{4}-x-2x^{6}+x^{2}+x^{7}. Factor out x.

$$x\left(2x-4x^{3}-1-2x^{5}+x+x^{6}\right)$$

Rewrite the complete factored expression. Polynomial x^{6}-2x^{5}-4x^{3}+3x-1 is not factored since it does not have any rational roots.

$$2x\left(x^{6}-2x^{5}-4x^{3}+3x-1\right)$$

Evaluate

$$2x\left(x^{6}-2x^{5}-4x^{3}+3x-1\right)$$

Solution Steps

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}-8x^{4}-2x-4x^{6}+2x^{7}$$