Answer:
B. (x+4)(x-4)
Step-by-step explanation:
We are given:
[tex]y=\frac{2x}{x^2-16}[/tex]
And asked to factor the denominator.
When factoring, you have a^2 + bx + c, and when wanting to turn it into a binomial, you have to find two numbers that multiply to c and add up to b.
In this case, we see that c is equal to -16. List out the factor of -16:
±1 , ±16
±2 , ±8
-4 , 4
Now we see that b is not present, therefore being 0. Our goal is to find two factors of -16 that will equal to 0 when added.
1 and 16 will never make 0
2 and 8 cannot make 0 either
4 and 4 can make 0, and since 16 is a negative number, one 4 needs to be negative while the other is a positive.
Basically stating, our factor of the denominator is:
[(x + 4)(x - 4)]