Find the domain
(x^3+10x^2+31x+30)/x^2-4

Question

Find the domain
(x^3+10x^2+31x+30)/x^2-4

anonymous · Answer

when will this function not exist? for what values of x will the function be undefined?

anonymous · Answer

$$\frac{ x^3+10x^2+31x+30 }{ x^2-4 }$$

anonymous · Answer

I have -2 and 2, but I don't understand why I don't include them.

anonymous · Answer

if for example you get X/0 or and number over zero you function will be undefined so you want to know when the denominator will equal zero

anonymous · Answer

Oh, duh, I remember that.

anonymous · Answer

if the denominator is zero your function is undefined so you set the denominator equal to zero 
x^2-4=0
x^2=4
x=+-2 so x=2 and x=-2 will both result in zero in the denominator which is undefined so these values arn't included in the domain

anonymous · Answer

So would I write that in interval notation or would this work:
$${x|x \neq-2,2}$$

anonymous · Answer

Also, if there's a case where I get an imaginary number, would I disregard it as a "problem" in the domain?

anonymous · Answer

When you have square roots or other even roots you need to know when the value under the radical is negative and exclude all of those values.

anonymous · Answer

complex values as solutions don't effect the domain.

anonymous · Answer

Thank you. You're a fab helper! :)