Question

How do you find the zeros for the function `f(x)=(x^2-x-6)/(x^2+8x+12)`?

Answer 1

The zero is `3`.

Explanation:

Usually, when dealing with a function made up of a fraction of two polynomials, you only need to find the zeros of the numerator since zero divided by anything is always zero. One thing to be cautious about in this problem is that the zeros for the numerator cannot be zeros for the denominator. If that happens, you are then dealing with a hole in the graph rather than a zero.

In this problem, when you factor the top, you get `(x-3)(x+2)` so your possible zeros are `3` and -`2`, but when you factor the bottom you get `(x+2)(x+6)` meaning that if you were to plug -`2` into your original equation, your answer would be undefined, so your only zero would be `3`.