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

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Answer 1 · 2015-05-06T20:07:50

Factor by grouping

$x^3+x^2-x-1 =[x^3+x^2]+[-x-1]$

The first bracket has a common factor of $x^2$ and the second bracket has a common factor of $-1$ . take those out to get:

$x^3+x^2-x-1 = x^2[x+1] color(red)(+) (-1)[x+1]$

Now we have two terms, one on each side of the red $color(red)(+)$ .

Each term has a factor (in brackets) of $[x+1]$ . Tlhat is a common factor, so we can factor it out:

$x^3+x^2-x-1 = x^2[x+1] color(red)(+) (-1)[x+1]$

$color(white)"ssssssssssssssssss"$ $=( x^2 color(red)(+) (-1))[x+1]$

$color(white)"ssssssssssssssssss"$ $=( x^2 - 1)(x+1)$

$x^3+x^2-x-1 = ( x^2 - 1)(x+1)$

Are we finished or can anything be factored more?

$x^2-1$ is a difference of twp squares, so we can factor it.

$x^3+x^2-x-1 = ( x+1)(x - 1)(x+1)$

Now we are finished.

How do you factor x^3+x^2-x-1x^3+x^2-x-1?