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

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Answer 1 · 2015-05-25T16:07:24

$x^3+x^2-x-1$

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

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

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

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

$=(x-1)(x+1)(x+1)$

...using the difference of squares identity

$(a^2-b^2) = (a-b)(a+b)$

Answer 2 · 2017-12-31T13:51:27

Find a useful grouping, then factor.

Answer: $(x + 1)^2 (x - 1)$

Factor $x^3+x^2−x−1$

The idea of grouping $x^2$ with - $1$ looks really tempting
because it's the Difference of Two Squares..

1) Find a useful grouping
$(x^3 - x) + (x^2 - 1)$

2) Factor each group
$x (x^2 - 1) +1 (x^2 - 1)$

3) Factor out $(x^2 - 1)$ from each group
$(x^2 - 1)(x + 1)$

4) Factor $(x^2 - 1)$ as the Difference of Two Squares
$(x - 1)(x + 1)(x + 1)$ $larr$ answer

5) You can write it this way if you want:
$(x + 1)^2 (x - 1)$ $larr$ same answer

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