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

##### 1 Answer

Nov 29, 2015

#### Answer:

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

#### Explanation:

First notice that the sum of the coefficients is

Divide by

Then factor the remaining quadratic factor - recognisable as a perfect square trinomial.

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

A little trick to spot that