MATH SOLVE

3 months ago

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

Accepted Solution

A:

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!