# How do you factor x^3+x^2+x+1 by grouping?

Mar 16, 2017

See the entire solution process below:

#### Explanation:

First, group the two terms on the left and the two terms on the right as:
$\left({x}^{3} + {x}^{2}\right) + \left(x + 1\right)$

Now, factor out an ${x}^{2}$ from the term on the left to give:

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

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

$\left(x + 1\right)$ can also be written as $1 \left(x + 1\right)$ giving:

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

We can now factor out an $\left(x + 1\right)$ from each term giving:

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