Question

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

Answer 1

Answer:

The correct option is 2.

Step-by-step explanation:

The given expression is

$6x^3+6$

Taking gout the common factors.

$6(x^3+1)$

It can be written as

$6(x^3+1^3)$

$6(x+1)(x^2-x+1)$            $[\because a^3+b^3=(a+b)(a^2-ab+b^2)]$

It means 6, (x+1) and $(x^2-x+1)$ is factors of given expression.

Therefore the correct option is 2.

Answer 2

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