#x^3 - x^2 - x + 1#
To factor this, we have to do it by grouping terms:
#(x^3-x^2) + (-x+1)#
To factor #x^3 - x^2#, we have to see the greatest factor that both expressions have in common. In this case, that is #x^2#. So the factored form would be:
#x^2(x-1)#
For the second part, we want #-x# to be positive, so we can factor out a #-1#:
#-1(x-1)#
Now combine them:
#x^2(x-1)-1(x-1)#
This becomes:
#(x^2-1)(x-1)#
If you want, you can still factor this further since #(x^2-1)# can split out to be #(x-1)(x+1)#. So the factored form is:
#(x-1)(x+1)(x-1)#
Hope this helps!
