Choose one of the factors of 6x3 + 6. x − 1 x + 1 x2 − 2x + 1 x2 + x + 1

First thing to do is factor out the common 6 to get  .  We have set it equal to 0 so we can solve for the solutions of the polynomial.  By the Zero Product Property, either 6 = 0  or  .  Of course we know that 6 does not equal 0, so that's not a solution.  So  .  Solving for x, we have  .  Taking the cubed root of both sides gives us  .  Because the index on our radical is an odd number, 3, we are "allowed" to take the negative of the radicand.  The cubed root of -1 is -1, since -1^3 = -1.  Therefore, our root is x = -1.  Our factor, then is x + 1.  Your choice is the second one down.  There you go!