Solve x^3+x^2+xxxxx

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

Evaluate

$$x^{2}\left(x^{3}+x+1\right)$$

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Factor

$$x^{2}\left(x^{3}+x+1\right)$$

Solution Steps

Factor out x.

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

Consider x^{2}+x+x^{4}. Factor out x.

$$x\left(x+1+x^{3}\right)$$

Rewrite the complete factored expression. Polynomial x+1+x^{3} is not factored since it does not have any rational roots.

$$xx\left(x+1+x^{3}\right)$$