Answer: a. [tex]g(x)=x^2-2x-8[/tex]
Step-by-step explanation:
You know that the zeros of the function g(x) are:
[tex]x=-2\\x=4[/tex]
Then, the factored form must be:
[tex](x+2)(x-4)=0[/tex]
Now, applying the Distributive property:
[tex](x+2)(x-4)=0\\\\(x)(x)+(x)(2)+(x)(-4)+(2)(-4)=0\\\\x^2+2x-4x-8=0[/tex]
Finally, adding the like terms, you get:
[tex]x^2-2x-8=0[/tex]
Therefore, the function g(x) is:
[tex]g(x)=x^2-2x-8[/tex]
