Solve (x^3+x+2)+(3x^5-x^4+2x^3+5{x}^2+x-2)

$$( { x }^{ 3 } +x+2)+(3 { x }^{ 5 } - { x }^{ 4 } +2 { x }^{ 3 } +5 { x }^{ 2 } +x-2)$$

Evaluate

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

Solution Steps

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

$$3x^{3}+x+2+3x^{5}-x^{4}+5x^{2}+x-2$$

Combine x and x to get 2x.

$$3x^{3}+2x+2+3x^{5}-x^{4}+5x^{2}-2$$

Subtract 2 from 2 to get 0.

$$3x^{3}+2x+3x^{5}-x^{4}+5x^{2}$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$3x^{5}-x^{4}+3x^{3}+5x^{2}+2x$$

Factor out x. Polynomial 3x^{4}-x^{3}+3x^{2}+5x+2 is not factored since it does not have any rational roots.

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