Firstly, set g(x) to zero: [tex]0=x^2-25[/tex]
So for this, we will be factoring this function using the difference of squares. The difference of squares is [tex]x^2-y^2=(x+y)(x-y)[/tex] . Using our function, apply this as such:
[tex]x^2-25=(x+5)(x-5)\\0=(x+5)(x-5)[/tex]
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:
[tex]x+5=0\\x=-5\\\\x-5=0\\x=5[/tex]
The zeros of this function are 5 and -5. The correct option is C.
