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.
