Question

What are all the zeros of the function g(x)=

Answer 1

Firstly, set g(x) to zero:
`0=x^2-25`

So for this, we will be factoring this function using the difference of squares. The difference of squares is
`x^2-y^2=(x+y)(x-y)` . Using our function, apply this as such:

`x^2-25=(x+5)(x-5)\\0=(x+5)(x-5)`

Next, we are going to apply the Zero Product Property, which states that "if a × b = 0, then either a or b = 0 or both a and b = 0." In this case, a = x + 5 and b = x - 5. Solve each for zero:

`x+5=0\\x=-5\\\\x-5=0\\x=5`

The zeros of this function are 5 and -5. The correct option is C.