Question 119398


{{{x^3+x^2-x-1}}} Start with the given expression


{{{(x^3+x^2)+(-x-1)}}} Group like terms



{{{x^2(x+1)-1(x+1)}}} Factor out the GCF {{{x^2}}} out of the first group. Factor out the GCF {{{-1}}} out of the second group



{{{(x^2-1)(x+1)}}} Since we have the common term {{{x+1}}}, we can combine like terms



{{{(x-1)(x+1)(x+1)}}} Now factor {{{x^2-1}}} by using the difference of squares




{{{(x-1)(x+1)^2}}} Multiply




So {{{x^3+x^2-x-1}}} factors to {{{(x-1)(x+1)^2}}}