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

Accepted Solution

First thing to do is factor out the common 6 to get  [tex]6(x^3+1)=0[/tex].  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  [tex]x^3+1=0[/tex].  Of course we know that 6 does not equal 0, so that's not a solution.  So  [tex]x^3+1=0[/tex].  Solving for x, we have  [tex]x^3=-1[/tex].  Taking the cubed root of both sides gives us  [tex]x= \sqrt[3]{-1} [/tex].  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!