Question

Factor the denominator

Answer 1

B. (x+4)(x-4)

Explanation:

We are given:

`y=(2x)/(x^2-16)`

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)]