Solve x^2*x+x^2+x+1

$${ x }^{ 2 } \times x+ { x }^{ 2 } +x+1$$

Factor

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

Solution Steps

Multiply and combine like terms.

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

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

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

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

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

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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