Solve (5x^3-x^2+1)+(x^3+x^2+x-1)

$$( 5 x ^ { 3 } - x ^ { 2 } + 1 ) + ( x ^ { 3 } + x ^ { 2 } + x - 1 )$$

Evaluate

$$6x^{3}+x$$

Solution Steps

Combine 5x^{3} and x^{3} to get 6x^{3}.

$$6x^{3}-x^{2}+1+x^{2}+x-1$$

Combine -x^{2} and x^{2} to get 0.

$$6x^{3}+1+x-1$$

Subtract 1 from 1 to get 0.

$$6x^{3}+x$$

Factor

$$x\left(6x^{2}+1\right)$$

Solution Steps

Multiply and combine like terms.

$$6x^{3}+x$$

Factor out x. Polynomial 6x^{2}+1 is not factored since it does not have any rational roots.

$$x\left(6x^{2}+1\right)$$