Solve (-x^4+x^2-x-x^3+1)+(x^2-2{x}^3+4x-1)

$$(- { x }^{ 4 } + { x }^{ 2 } -x- { x }^{ 3 } +1)+( { x }^{ 2 } -2 { x }^{ 3 } +4x-1)$$

Evaluate

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

Solution Steps

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

$$-x^{4}+2x^{2}-x-x^{3}+1-2x^{3}+4x-1$$

Combine -x^{3} and -2x^{3} to get -3x^{3}.

$$-x^{4}+2x^{2}-x-3x^{3}+1+4x-1$$

Combine -x and 4x to get 3x.

$$-x^{4}+2x^{2}+3x-3x^{3}+1-1$$

Subtract 1 from 1 to get 0.

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

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

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