Question 154125
{{{x^3 -x^2 +ax+x-a - 1}}} Start with the given expression



{{{(x^3 -x^2)+(ax-a)+(x - 1)}}} Regroup the terms. This is not the only way to group them, but notice how the first two groups have something in common.



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



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



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



If you want to, you can expand {{{(x^2+a+1)(x-1)}}} to get {{{x^3 -x^2 +ax+x-a - 1}}} to verify your answer.