Solve a^4+a^3+a^2+a

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

Factor

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

Solution Steps

Factor out a.

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

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

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

Factor out common term a+1 by using distributive property.

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

Rewrite the complete factored expression. Polynomial a^{2}+1 is not factored since it does not have any rational roots.

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

Evaluate

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