Question

What are the excluded values for `(12a)/(a^2-3a-10)`?

Answer 1

`a=-2 and a=5`

Explanation:

In the expression `(12a)/(a^2-3a-10)` the denominator is a quadratic polynomial, that can be factored

`a^2-3a-10=a^2+(2-5)a+(-5)(2)`

`=a^2+2a-5a+(-5)(2)=(a-5)(a+2)`

Then

`(12a)/(a^2-3a-10)=(12a)/((a-5)(a+2))`

The zeroes of the polynomial in the denominator are `a=5` and `a=-2` which are the excluded values. These values are themselves excluded because you cannot divide by `0`.