Question 775732
The obvious factor is (2x-1).  If it is difficult to look at, try a substitution.  Let p=2x-1.


{{{p^2(x-3)+(x+1)p^3}}}
{{{p^2(x-3+(x+1)p)}}}
Put back the full expression substituted:
{{{(2x-1)^2(x-3+(x+1)(2x-1)))}}}
{{{(2x-1)^2(x-3+2x^2+2x-x-1)}}}
{{{(2x-1)^2(2x^2+2x-1)}}}