Solve (2x^3+x^2-5)+(x^2+x+6)

$$( 2 x ^ { 3 } + x ^ { 2 } - 5 ) + ( x ^ { 2 } + x + 6 )$$

Evaluate

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

Solution Steps

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

$$2x^{3}+2x^{2}-5+x+6$$

Add -5 and 6 to get 1.

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

Do the grouping 2x^{3}+2x^{2}+x+1=\left(2x^{3}+2x^{2}\right)+\left(x+1\right), and factor out 2x^{2} in 2x^{3}+2x^{2}.

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

Factor out common term x+1 by using distributive property. Polynomial 2x^{2}+1 is not factored since it does not have any rational roots.

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