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

Question

35509 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-16T01:54:48

See the entire solution process below:

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

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

$((x^2 xx x) + (x^2 xx 1)) + (x + 1)$

$x^2(x + 1) + (x + 1)$

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

$x^2(x + 1) + 1(x + 1)$

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

$(x + 1)(x^2 + 1)$

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